Introduction to digital signal processing 2
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Introduction to digital signal processing 2
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Introduction to digital signal processing 2
- 1. Hossam Fadeel National Telecommunication Institute 2010-2011
- 2. Objectives List the essential elements in a digital signal processing system Explain how analog signals are converted to digital form Discuss the purpose of filtering Describe the sampling process State the purpose of analog-to-digital conversion Explain how several types of ADCs operate Explain the basic concepts of a digital signal processor (DSP) Describe the basic architecture of a DSP Name some of the functions that a DSP performs State the purpose of digital-to-analog conversion Explain how DACs operate
- 3. Lecture Sessions 3 Digital Signal Processing Basics Converting Analog Signals to Digital Analog-to-Digital Conversion Methods The Digital Signal Processor (DSP) Digital-to-Analog Conversion Methods
- 4. Introduction Digital signal processing is a powerful technology that is widely used in many applications, such as automotive, consumer, graphics/imaging, industrial, instrumentation, medical, military, telecommunications, and voice/speech applications. Digital signal processing incorporates mathematics, software programming, and processing hardware to manipulate analog signals. This presentation provide a brief look at digital signal processing. To completely cover the topic in depth a list of references is available at the last slide. Much information, including datasheets about DSPs can be found on Manufacturer websites like: Texas Instruments: www.ti.com Motorola: www.motorola.com Analog Devices: www.analogdevices.com
- 5. Section 1: DIGITAL SIGNAL PROCESSING BASICS
- 6. DIGITAL SIGNAL PROCESSING BASICS Digital signal processing converts signals that naturally occur in analog form, such as sound, video, and information from sensors, to digital form and uses digital techniques to enhance and modify analog signal data for various applications. A digital signal processing system first translates a continuously varying analog signal into a series of discrete levels. This series of levels follows the variations of the analog signal and resembles a staircase, as illustrated for the case of a sine wave in Figure-1. The process of changing the original analog signal to a "stairstep" approximation is accomplished by a sample- and-hold circuit.
- 7. DIGITAL SIGNAL PROCESSING BASICS Next, the "stairstep" approximation is quantized into binary codes that represent each discrete step on the "stairsteps" by a process called analog-to-digital (A/D) conversion. Once the analog signal has been converted to a binary coded form, it is applied to a DSP (digital signal processor).
- 8. DIGITAL SIGNAL PROCESSING BASICS The DSP can perform various operations on the incoming data, such as: removing unwanted interference increasing the amplitude of some signal frequencies and reducing others encoding the data for secure transmissions, and detecting and correcting errors in transmitted codes. After a DSP processes a signal, the signal can be converted back to a much improved version of the original analog signal. This is accomplished by a digital-to-analog converter (DAC).
- 9. DIGITAL SIGNAL PROCESSING BASICS Anti- aliasing filter Sample and Hold circuit ADC DSP DAC Reconstructio n filter Figure-2 Basic block diagram of a typical digital signal processing system. 00010 01101 10011 00010 01101 10011
- 10. DIGITAL SIGNAL PROCESSING BASICS DSPs are actually a specialized type of microprocessor but are different from general- purpose microprocessors in a couple of significant ways. Typically, microprocessors are designed for general- purpose functions and operate with large software packages. DSPs are used for special-purpose applications; they are very fast number crunchers that must work in real time by processing information as it happens using specialized algorithms (programs).
- 11. Review What does DSP stand for? What does ADC stand for? What does DAC stand for?
- 12. Section 2: CONVERTING ANALOG SIGNALS TO DIGITAL
- 13. CONVERTING ANALOG SIGNALS TO DIGITAL In order to process signals using digital techniques, the incoming analog signal must be converted into digital form. Sampling is the process of taking a sufficient number of discrete values at points on a waveform that will define the shape of waveform. The more samples you take, the more accurately you can define a waveform. Sampling converts an analog signal into a series of impulses, each representing the amplitude of the signal at a given instant in time. Before a signal can be sampled, it must be passed through a low-pass filter (anti-aliasing filter) to eliminate harmonic frequencies above a certain value as determined by the
- 14. CONVERTING ANALOG SIGNALS TO DIGITAL The sampling theorem states that, in order to represent an analog signal, the sampling frequency, fsample, must be at least twice the highest frequency component fa(max) of the analog signal. The frequency fa(max) is known as the Nyquist frequency and is expressed in Equation -1. In practice, the sampling frequency should be more than twice the highest analog frequency.
- 15. CONVERTING ANALOG SIGNALS TO DIGITAL Figure -3 illustrates the process of sampling.
- 16. CONVERTING ANALOG SIGNALS TO DIGITAL The Need for Filtering Low-pass filtering is necessary. An alias is a signal produced when the sampling frequency is not at least twice the signal frequency. If the analog signal contains frequencies above the Nyquist frequency, these frequencies overlap into the spectrum of the sample waveform as shown and interference occurs.
- 17. CONVERTING ANALOG SIGNALS TO DIGITAL To avoid an aliasing error, the filter must at least eliminate all analog frequencies above the minimum frequency in the sampling spectrum, as illustrated in Figure -5. Aliasing can also be avoided by sufficiently increasing the sampling frequency. However, the maximum sampling frequency is usually limited by the performance of the analog-to-digital converter (ADC) that follows it.
- 18. CONVERTING ANALOG SIGNALS TO DIGITAL The holding operation is part of the sample-and-hold block shown in Figure -2. After filtering and sampling, the sampled level must be held constant until the next sample occurs. This is necessary for the ADC to have time to process the sampled value.
- 19. CONVERTING ANALOG SIGNALS TO DIGITAL Analog-to-digital conversion is the process of converting the output of the sample-and- hold circuit to a series of binary codes that represent the amplitude of the analog input at each of the sample times.
- 20. CONVERTING ANALOG SIGNALS TO DIGITAL The process of converting an analog value to a code is called quantization. During the quantization process, the ADC converts each sampled value of the analog signal to a binary code. The more bits that are used to represent a sampled value, the more accurate is the representation.
- 21. CONVERTING ANALOG SIGNALS TO DIGITAL If the resulting 2-bit digital codes are used to reconstruct the original waveform, which is done by digital-to-analog converters (DAC), you would get the waveform shown in Figure -9. As you can see, quite a bit of accuracy is lost using only two bits to represent the sampled values.
- 22. CONVERTING ANALOG SIGNALS TO DIGITAL
- 23. CONVERTING ANALOG SIGNALS TO DIGITAL
- 24. Review What does sampling mean? Why must you hold a sampled value? If the highest frequency component in an analog signal is 20 kHz, what is the minimum sample frequency? What does quantization mean? What determines the accuracy of the quantization process?
- 26. ANALOG-TO-DIGITAL CONVERSION METHODS Analog-to-digital conversion is the process by which an analog quantity is converted to digital form. It is necessary when measured quantities must be in digital form for processing or for display or storage. Two important ADC parameters are resolution, and throughput. Resolution: which is the number of bits Throughput: is the sampling rate an ADC can handle in units of samples per second (sps).
- 27. ANALOG-TO-DIGITAL CONVERSION METHODS Flash (Simultaneous) Analog-to-Digital Converter The flash method utilizes comparators that compare reference voltages with the analog in-put voltage. When the input voltage exceeds the reference voltage for a given comparator, a HIGH is generated. In general, 2n - 1 comparators are required for conversion to an n-bit binary code. The number of bits used in an ADC is its resolution. The large number of comparators necessary for a reasonable-sized binary number is one of the disadvantages of the Dash ADC. Its chief advantage is that it provides a fast conversion time because of a high throughput. The reference voltage for each comparator is set by the resistive voltage- divider circuit. The output of each comparator is connected to an input of the priority encoder. The encoder is enabled by a pulse on the EN input. and a 3-bit code representing the value of the input appears on the encoder's outputs. The binary code is determined by the highest-order input having a HIGH level.
- 30. Section 4: THE DIGITAL SIGNAL PROCESSOR (DSP)
- 31. THE DIGITAL SIGNAL PROCESSOR (DSP) Essentially, a digital signal processor (DSP) is a special type of microprocessor that processes data in real time. Its applications focus on the processing of digital data that represents analog signals. A DSP, like a microprocessor, has a central processing unit (CPU) and memory units in addition to many interfacing functions. The digital signal processor (DSP) is the heart of a digital signal processing system.
- 32. THE DIGITAL SIGNAL PROCESSOR (DSP) Sound cards used in computers use an ADC to convert sound from a microphone, audio CD player, or other source into a digital signal. The ADC sends the digital signal to a digital signal processor (DSP). Based on instructions from a ROM, one function of the DSP is to compress the digital signal so it uses less storage space. The DSP then sends the compressed data to the computer's processor which, in turn, sends the data to a hard drive or CD ROM for storage. To playa recorded sound, the stored data is retrieved by the processor and sent to the DSP where it is decompressed and sent to a DAC. The output of the DAC I which is a reproduction of the original sound signal, is applied to the speakers. COMPUTER NOTE
- 33. THE DIGITAL SIGNAL PROCESSOR (DSP) DSP Programming DSPs are typically programmed in either assembly language or in C. assembly language is used much more in DSPs than in general- purpose microprocessors. DSP programs are usually much shorter than traditional microprocessor programs because of their very specialized applications DSP Applications The DSP, unlike the general-purpose microprocessor, must typically process data in real time; that is, as it happens. Many applications in which DSPs are used cannot tolerate any noticeable delays, requiring the DSP to be extremely fast. In addition to cell phones, digital signal processors (DSPs) are used in multimedia computers, video recorders, CD players, and disk drivers, digital radio modems, and other applications to improve the signal quality. Also, DSPs are becoming more common in television applications.
- 34. THE DIGITAL SIGNAL PROCESSOR (DSP) Telecommunications Speech Generation and Recognition Radar Image Processing Filtering DSP Applications
- 36. References Dahnoun, Nairn. Digital Signal Processing Implementation Using the TMS320C6000 DSP Hayes, Monson. Schaum's Outline of Digital Signal Processing. Kuo, Sen, and Bob Lee. Real-Time Digital Signal Processing: Implementations. Applications. and Experiments with the TMS320C55x. Lyons, Richard. Understanding Digital Signal Processing. Marven, Craig, and Gillian Ewers. A Simple Approach to Digital Signal Processing. New York: John Wiley & Sons. 1996. Oppenheim, Alan, and Ronald Schafer. Digital Signal Processing. Orfanidis. Sophocles. introduction to Signal Processing. Proakis, John, and Dimitris Manolakis. Digital Signal Processing: Principles, Algorithms, and Applications, 3d ed. Steiglitz, Ken. Digital Signal Processing Primer: With Applications to Digital Audio and Computer Music. Williams, Douglas, and Vijay Madisetti. Digital Signal Processing Handbook.
Hinweis der Redaktion
- CHAPTER OBJECTIVES List the essential elements in a digital signal processing system Explain how analog signals are converted to digital form Discuss the purpose of filtering Describe the sampling process State the purpose of analog-to-digital conversion Explain how several types of ADCs operate Explain the basic concepts of a digital signal processor (DSP) Describe the basic architecture of a DSP Name some of the functions that a DSP performs State the purpose of digital-to-analog conversion Explain how DACs operate
- 1 Digital Signal Processing Basics 2 Converting Analog Signals to Digital 3 Analog-to-Digital Conversion Methods 4 The Digital Signal Processor (DSP) 5 Digital-to-Analog Conversion Methods
- Next, the "stairstep" approximation is quantized into binary codes that represent each discrete step on the "stairsteps" by a process called analog-to-digital (A/D) conversion. The circuit that performs A/D conversion is an analog-to-digital converter (ADC). Once the analog signal has been converted to a binary coded form, it is applied to a DSP (digital signal processor).
- The DSP can perform various operations on the incoming data, such as removing unwanted interference, increasing the amplitude of some signal frequencies and reducing others, encoding the data for secure transmissions, and detecting and correcting errors in transmitted codes. DSPs make possible, among many other things, the cleanup of sound recordings, the removal of echos from communications lines, the enhancement of images from CT scans for better medical diagnosis, and the scrambling of cellular phone conversations for privacy. After a DSP processes a signal, the signal can be converted back to a much improved version of the original analog signal. This is accomplished by a digital-to-analog converter (DAC). Figure 13-2 shows a basic block diagram of a typical digital signal processing system.
- DSPs are actually a specialized type of microprocessor but are different from general- purpose microprocessors in a couple of significant ways. Typically, microprocessors are designed for general-purpose functions and operate with large software packages. DSPs are used for special-purpose applications; they are very fast number crunchers that must work in real time by processing information as it happens using specialized algorithms (programs). The analog-to-digital converter (ADC) in a system must take samples of the incoming analog data often enough to catch all the relevant fluctuations in the signal amplitude, and the DSP must keep pace with the sampling rate of the ADC by doing its calculations as fast as the sampled data are received. Once the digital data are processed by the DSP, they go to the digital-to-analog converter (DAC) for conversion back to analog form.
- What does DSP stand for? What does ADC stand for? What does DAC stand for? An analog signal is changed to a binary coded form by what circuit? A binary coded signal is changed to analog form by what circuit?
- Sampling and Filtering The first two blocks in the system diagram of Figure 13-2 are the anti-aliasing filter and the sample-and-hold circuit. The sample-and-hold function does two operations, the first of which is sampling. Sampling is the process of taking a sufficient number of discrete values at points on a waveform that will define the shape of waveform. The more samples you take, the more accurately you can define a waveform. Sampling converts an analog signal into a series of impulses, each representing the amplitude of the signal at a given instant in time. Figure -3 illustrates the process of sampling. When an analog signal is to be sampled, there are certain criteria that must be met in order to accurately represent the original signal. All analog signals (except a pure sine wave) contain a spectrum of component frequencies called harmonics. The harmonics of an analog signal are sine waves of different frequencies and amplitudes. When the harmonics of a given periodic waveform are added, the result is the original signal. Before a signal can be sampled, it must be passed through a low-pass filter (anti-aliasing filter) to eliminate harmonic frequencies above a certain value as determined by the Nyquist frequency.
- The Sampling Theorem Notice in Figure 13-3 that there are two input waveforms. One is the analog signal and the other is the sampling pulse waveform. The sampling theorem states that, in order to represent an analog signal, the sampling frequency, fsample, must be at least twice the highest frequency component fa(max) of the analog signal. Another way to say this is that the highest analog frequency can be no greater than one-half the sampling frequency. The frequency fa(max) is known as the Nyquist frequency and is expressed in Equation 13-1. In practice, the sampling frequency should be more than twice the highest analog frequency.
- The Need for Filtering Low-pass filtering is necessary to remove all frequency components (harmonics) of the analog signal that exceed the Nyquist frequency. If there are any frequency components in the analog signal that exceed the Nyquist frequency, an unwanted condition known as aliasing will occur. An alias is a signal produced when the sampling frequency is not at least twice the signal frequency. An alias signal has a frequency that is less than the highest frequency in the analog signal being sampled and therefore falls within the spectrum or frequency band of the input analog signal causing distortion. Such a signal is actually "posing" as part of the analog signal when it really isn't. thus the term alias. Another way to view aliasing is by considering that the sampling pulses produce a spectrum of harmonic frequencies above and below the sample frequency, as shown in Figure 13-5. If the analog signal contains frequencies above the Nyquist frequency, these frequencies overlap into the spectrum of the sample waveform as shown and interference occurs. The lower frequency components of the sampling waveform become mixed in with the frequency spectra of the analog waveform, resulting in an aliasing error.
- A low-pass anti-aliasing filter must be used to limit the frequency spectrum of the analog signal for a given sample frequency. To avoid an aliasing error, the filter must at least eliminate all analog frequencies above the minimum frequency in the sampling spectrum, as illustrated in Figure 13-6. Aliasing can also be avoided by sufficiently increasing the sampling frequency. However, the maximum sampling frequency is usually limited by the performance of the analog-to-digital converter (ADC) that follows it.
- The holding operation is part of the sample-and-hold block shown in Figure -2. After filtering and sampling, the sampled level must be held constant until the next sample occurs. This is necessary for the ADC to have time to process the sampled value. This sample-and hold operation results in a "stairstep" waveform that approximates the analog input waveform, as shown in Figure 13-7.
- Analog-to-digital conversion is the process of converting the output of the sample-and- hold circuit to a series of binary codes that represent the amplitude of the analog input at each of the sample times. The sample-and-hold process keeps the amplitude of the analog input signal constant between sample pulses; therefore, the analog-to-digital conversion can be done using a constant value rather than having the analog signal change during a conversion interval, which is the time between sample pulses. Figure 13-7 illustrates the basic function of an analog-to-digital (ADC) converter. The sample intervals are indicated by dashed lines.
- Quantization The process of converting an analog value to a code is called quantization. During the quantization process, the ADC converts each sampled value of the analog signal to a binary code. The more bits that are used to represent a sampled value, the more accurate is the representation. To illustrate, let's quantize a reproduction of the analog waveform into four levels (0-3). As shown in Figure 13-9, two bits are required. Note that each quantization level is represented by a 2-bit code on the vertical axis, and each sample interval is numbered along the horizontal axis. The quantization process is summarized in Table 13-1. If the resulting 2-bit digital codes are used to reconstruct the original waveform, which is done by digital-to-analog converters (DAC), you would get the waveform shown in Figure 13-10. As you can see, quite a bit of accuracy is lost using only two bits to represent the sampled values.
- Now, let's see how more bits will improve the accuracy. Figure-10 shows the same waveform with sixteen quantization levels (4 bits). The 4-bit quantization process is summarized in Table -2.
- If the resulting 4-bit digital codes are used to reconstruct the original waveform, you would get the waveform shown in Figure -11. As you can see, the result is much more like the original waveform than for the case of four quantization levels in Figure 13-10. This shows that greater accuracy is achieved with more quantization bits. Most integrated circuit ADCs use from 8 to 24 bits, and the sample-and-hold function is some- times contained on the ADC chip. Several types of ADCs are introduced in the next section.
- What does sampling mean? Why must you hold a sampled value? If the highest frequency component in an analog signal is 20 kHz, what is the minimum sample frequency? What does quantization mean? What determines the accuracy of the quantization process?
- ANALOG-TO-DIGITAL CONVERSION METHODS
- As you have seen, analog-to-digital conversion is the process by which an analog quantity is converted to digital form. It is necessary when measured quantities must be in digital form for processing or for display or storage. Some common types of analog- to-digital converters (ADCs) are now examined. Two important ADC parameters are resolution, which is the number of bits, and throughput, which is the sampling rate an ADC can handle in units of samples per second (sps).
- Flash (Simultaneous) Analog-to-Digital Converter The flash method utilizes comparators that compare reference voltages with the analog in-put voltage. When the input voltage exceeds the reference voltage for a given comparator, a HIGH is generated. Figure 13-14 shows a 3-bit converter that uses seven comparator circuits; a comparator is not needed for the all-0s condition. A 4-bit converter of this type requires fifteen comparators. In general, 2n - 1 comparators are required for conversion to an n-bit binary code. The number of bits used in an ADC is its resolution. The large number of comparators necessary for a reasonable-sized binary number is one of the disadvantages of the Dash ADC. Its chief advantage is that it provides a fast conversion time because of a high throughput, measured in samples per second (sps). The reference voltage for each comparator is set by the resistive voltage-divider circuit. The output of each comparator is connected to an input of the priority encoder. The encoder is enabled by a pulse on the EN input. and a 3-bit code representing the value of the input appears on the encoder's outputs. The binary code is determined by the highest-order input having a HIGH level. The frequency of the enable pulses and the number of bits in the binary code determine the accuracy with which the sequence of binary codes represents the input of the ADC. There should be one enable pulse for each sampled level of the input signal.
- THE DIGITAL SIGNAL PROCESSOR (DSP)
- Essentially, a digital signal processor (DSP) is a special type of microprocessor that processes data in real time. Its applications focus on the processing of digital data that represents analog signals. A DSP, like a microprocessor, has a central processing unit (CPU) and memory units in addition to many interfacing functions. Every time you use your cellular telephone, you are using a DSP, and this is only one example of its many applications. The digital signal processor (DSP) is the heart of a digital signal processing system. It takes its input from an ADC and produces an output that goes to a DAC, as shown in Figure 13-28. As you have learned, the ADC changes an analog waveform into data in the form of a series of binary codes that are then applied to the DSP for processing. After being processed by the DSP, the data go to a DAC for conversion back to analog form.
- Sound cards used in computers use an ADC to convert sound from a microphone, audio CD player, or other source into a digital signal. The ADC sends the digital signal to a digital signal processor (DSP). Based on instructions from a ROM, one function of the DSP is to compress the digital signal so it uses less storage space. The DSP then sends the compressed data to the computer's processor which, in turn, sends the data to a hard drive or CD ROM for storage. To playa recorded sound, the stored data is retrieved by the processor and sent to the DSP where it is decompressed and sent to a DAC. The output of the DAC I which is a reproduction of the original sound signal, is applied to the speakers.
- DSP Programming DSPs are typically programmed in either assembly language or in C. Because programs written in assembly language can usually execute faster and because speed is critical in most DSP applications, assembly language is used much more in DSPs than in general-purpose microprocessors. Also, DSP programs are usually much shorter than traditional microprocessor programs because of their very specialized applications where much redundancy is used. In general, the instruction sets for DSPs tend to be smaller than for microprocessors. DSP Applications The DSP, unlike the general-purpose microprocessor, must typically process data in real time; that is, as it happens. Many applications in which DSPs are used cannot tolerate any noticeable delays, requiring the DSP to be extremely fast. In addition to cell phones, digital signal processors (DSPs) are used in multimedia computers, video recorders, CD players, and disk drivers, digital radio modems, and other applications to improve the signal quality. Also, DSPs are becoming more common in television applications. An important application of DSPs is in signal compression and decompression. In CD systems, for example. the music on the CD is in a compressed form so that it doesn't use as much storage space. It must be decompressed in order to be reproduced. Also signal compression is used in cell phones to allow a greater number of calls to be handled simultaneously in a local cell. Some other areas where it has had a major impact are as follows.
- Telecommunications The field of telecommunications involves transferring all types of information from one location to another, including telephone conversations. television signals, and digital data. Among other functions, the DSP facilitates multiplexing many signals onto one transmission channel because information in digital form is relatively easy to multiplex and demultiplex. At the transmitting end of a telecommunications system, DSPs are used to compress digitized voice signals for conservation of bandwidth. Compression is the process of reducing the data rate. Generally, a voice signal is converted to digital form at 8000 samples per second (sps), based on a Nyquist frequency of 4 kHz. If 8 bits are used to encode each sample, the data rate is 64 kbits/s. In general, reducing (compressing) the data rate from 64 kbits/s to 32 kbits/s results in no loss of sound quality. When the data are compressed to 8 kbits/s, the sound quality is reduced noticeably. When compressed to the minimum of 2 kbits/s, the sound is greatly distorted but still usable for some applications where only word recognition and not quality is important. At the receiving end of a telecommunications system, the DSP decompresses the data to restore the signal to its original form. Echoes, a problem in many long distance telephone connections, Occur when a portion of a voice signal is returned with a delay. For shorter distances, this delay is barely noticeable; but as the distance between the transmitter and the receiver increases, so does the delay time of the echo. DSPs are used to effectively cancel the annoying echo, which results in a clear, undisturbed voice signal. Music Processing The DSP is used in the music industry to provide filtering, signal addi- tion and subtraction, and signal editing in music preparation and recording. Also, another application of the DSP is to add artificial echo and reverberation, which are usually mini- mized by the acoustics of a sound studio, in order to simulate ideal listening environments from concert halls to small rooms. Speech Generation and Recognition DSPs are used in speech generation and recog- nition to enhance the quality of man/machine communication. The most common method used to produce computer-generated speech is digital recording. In digital recording, the human voice is digitized and stored, usually in a compressed form. During playback the stored voice data are ltncompressed and converted back into the original analog form. Approximately an hour of speech can be stored llsing about 3 MB of memory. Speech recognition is mllch more difficult to accomplish than speech generation. Even with today's computers. speech recognition is very limited and, with a few exceptions, the re- sults are only moderately successful. The DSP is used to isolate and analyze each word in the incoming voice signal. Certain parameters are identified in each word and compared with pre- vious examples of the spoken word to create the closest match. Most systems are limited to a few hundred words at best. Also, significant pauses between words are usually required and the system must be "trained" for a given individual's voice. Speech recognition is an area of tremendous research effort and will eventually be applied in many commercial applications. Radar In radio detection and ranging (radar) applications, DSPs provide more accurate determination of distance using dam compression techniques, decrease noise using filter- ing techniques, thereby increasing the range, and optimize the ability of the radar system to identity specific types of targets. DSPs are also used in similar ways in sonar systems. Image Processing The DSP is used in image-processing applications such as the com- puted tomography (CT) and magnetic resonance imaging (MRI), which are widely used in the medical field for looking inside the human body. In CT, X-rays are passed through a section of the body from many directions. The resulting signals are converted to digital form and stored. This stored information is used to produce calculated images that appear to be slices through the human body that show great detail and permit better diagnosis. Instead of X-rays, MRI uses magnetic fields in conjunction with radio waves to probe inside the human body. MRI produces images, just as CT, and provides excellent discrim- ination between different types of tissue as well as information such as blood flow through arteries. MRI depends entirely on digital signal processing methods. In applications such as video telephones. digital television, and other media that provide moving pictures, the DSP uses image compression to reduce the number of bits needed. making these systems commercially feasible. Filtering DSPs are commonly used to implement digital filters for the purposes of sepa- rating signals that have been combined with other signals or with interference and noise and for restoring signals that are distorted. Although analog filters are quite adequate for some applications, the digital filter is generally much superior in terms of the performance that can be achieved. One drawback to digital filters is that the execute time required produces a delay from the time the analog signal is applied until the time the output appears. Analog filters present no delay problems because as soon as the input occurs, the response appears on the output. Analog filters are also less expensive than digital filters. Regardless of this, the overall performance of the digital filter is far superior in many applications.