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by David
Skolnick and Noam Levine
Having heard a lot about digital signal
processing (DSP) technology, you may have wanted to find out what can be done
with DSP, investigate why DSP is preferred to analog circuitry for many types of
operations, and discover how to learn enough to design your own DSP system. This
article, the first of a series, is an opportunity to take a substantial first
step towards finding answers to your questions. This series is an introduction
to DSP topics from the point of view of analog system designers seeking
additional tools for handling analog signals. Designers reading this series can
learn about the possibilities of DSP to deal with analog signals and where to
find additional sources of information and assistance.
What is [a] DSP? In brief, DSPs are processors or microcomputers whose hardware, software, and instruction sets are optimized for high-speed numeric processing applications an essential for processing digital data representing analog signals in real time. What a DSP does is straightforward. When acting as a digital filter, for example, the DSP receives digital values based on samples of a signal, calculates the results of a filter function operating on these values, and provides digital values that represent the filter output; it can also provide system control signals based on properties of these values. The DSP’s high-speed arithmetic and logical hardware is programmed to rapidly execute algorithms modelling the filter transformation.
The combination of design elements arithmetic operators, memory
handling, instruction set, parallelism, data addressing that provide this
ability forms the key difference between DSPs and other kinds of processors.
Understanding the relationship between real-time signals and DSP calculation
speed provides some background on just how special this combination is. The
real-time signal comes to the DSP as a train of individual samples from an
analog-to-digital converter (ADC). To do filtering in real-time, the DSP must
complete all the calculations and operations required for processing each sample
(usually updating a process involving many previous samples) before the next
sample arrives. To perform high-order filtering of real-world signals having
significant frequency content calls for really fast processors. WHY USE A DSP?
To get an idea of the type of
calculations a DSP does and get an idea of how an analog circuit compares with a
DSP system, one could compare the two systems in terms of a filter function. The
familiar analog filter uses resistors, capacitors, inductors, amplifiers. It can
be cheap and easy to assemble, but difficult to calibrate, modify, and
maintain a difficulty that increases exponentially with filter order. For
many purposes, one can more easily design, modify, and depend on filters using a
DSP because the filter function on the DSP is software-based, flexible, and
repeatable. Further, to create flexibly adjustable filters with higher-order
response requires only software modifications, with no additional hardware
unlike purely analog circuits. An ideal bandpass filter, with the frequency
response shown in Figure 1, would have the following characteristics:
`
Figure 1. An ideal bandpass filter and second-order approximations.
Figure 2. Filter equations and delay-line representation.
Approximating an ideal filter consists of applying a transfer function with appropriate coefficients and a high enough order, or number of taps (considering the train of input samples as a tapped delay line). Figure 3 shows the response of a 90-tap FIR filter compared with sharp-cutoff Chebyshev filters of various orders. The 90-tap example suggests how close the filter can come to approximating an ideal filter. Within a DSP system, programming a 90-tap FIR filter like the one in Figure 3 is not a difficult task. By comparison, it would not be cost-effective to attempt this level of approximation with a purely analog circuit. Another crucial point in favor of using a DSP to approximate the ideal filter is long-term stability. With an FIR (or an IIR having sufficient resolution to avoid truncation-error buildup), the programmable DSP achieves the same response, time after time. Purely analog filter responses of high order are less stable with time.
Figure 3. 90-tap FIR filter response compared with those of sharp cutoff Chebyshev filters.
This sampling rate is determined by the amount of signal information that is needed for processing the signals adequately for a given application. In order for an ADC to provide enough samples to accurately describe the real-world signal, the sampling rate must be at least twice the highest-frequency component of the analog signal. For example, to accurately describe an audio signal containing frequencies up to 20 kHz, the ADC must sample the signal at a minimum of 40 kHz. Since arriving signals can easily contain component frequencies above 20 kHz (including noise), they must be removed before sampling by feeding the signal through a low-pass filter ahead of the ADC. This filter, known as an anti-aliasing filter, is intended to remove the frequencies above 20 kHz that could corrupt the converted signal.
However, the anti-aliasing filter has a finite frequency rolloff, so additional bandwidth must be provided for the filter’s transition band. For example, with an input signal bandwidth of 20 kHz, one might allow 2 to 4 kHz of extra bandwidth.
Figure 4. Antialiasing filter ideal response.
Processing speed at a required sample rate is influenced by algorithm complexity. As a rule, the DSP needs to finish all operations relating to the first sample before receiving the second sample. The time between samples is the time budget for the DSP to perform all processing tasks. For the audio example, a 48-kHz sampling rate corresponds to a 20.833-µs sampling interval. Figure 5 relates the analog signal and digital sampling rate.
Figure 5. Sampling train and processing time.
Thus if all of the time between samples is available for operations to
implement the algorithm, a processor with a performance level of 2.4 MOPS is
required. Note that the two common ratings for DSPs, based on operations per
second (MOPS) and instructions per second (MIPS), are not the same. A processor
with a 10-MIPS rating that can perform 8 operations per instruction has
basically the same performance as a faster processor with a 40 MIPS rating that
can only perform 2 operations per instruction. SAMPLING
VARIOUS REAL-WORLD SIGNALS
There are two basic ways to acquire
data, either one sample at a time or one frame at a time (continuous processing
vs. batch processing). Sample-based systems, like a digital filter, acquire data
one sample at a time. As shown in Figure 6, at each tick of the clock, a sample
comes into the system and a processed sample is output. The output waveform
develops continuously.
Figure 6. Example of continuous processing of samples in digital filter.
Frame-based systems, like a spectrum analyzer, which determines the frequency components of a time-varying waveform, acquire a frame (or block of samples). Processing occurs on the entire frame of data and results in a frame of transformed data, as shown in Figure 7.
Figure 7. Example of batch processing of a block of data.
For an audio sampling rate of 48 kHz, a processor working on a frame of 1024
samples has a frame acquisition interval of 21.33 ms (i.e., 1024 x 20.833 µs =
21.33 ms). Here the DSP has 21.33 ms to complete all the required processing
tasks for that frame of data. If the system handles signals in real time, it
must not lose any data; so while the DSP is processing the first frame, it must
also be acquiring the second frame. Acquiring the data is one area where special
architectural features of DSPs come into play: Seamless data acquisition is
facilitated by a processor’s flexible data-addressing capabilities in
conjunction with its direct memory-accessing (DMA) channels. RESPONDING TO REAL-WORLD SIGNALS
One cannot
assume that all the time between samples is available for the execution of
processing instructions. In reality, time must be budgeted for the processor to
respond to external devices, controlling the flow of data in and out. Typically,
an external device (such as an ADC) signals the processor using an interrupt.
The DSP’s response time to that interrupt, or interrupt latency, directly
influences how much time remains for actual signal processing.
Interrupt latency (response delay) depends on several factors; the most dominant is the DSP architecture’s instruction pipelining. An instruction pipeline consists of the number of instruction cycles that occur between the time an interrupt is received and the time that program execution resumes. More pipeline levels in a DSP result in longer interrupt latency. For example, if a processor has a 20-ns cycle time and requires 10 cycles to respond to an interrupt, 200 ns elapse before it executes any signal-processing instructions.
When data is acquired one sample at a time, this 200-ns overhead will not
hurt if the DSP finishes the processing of each sample before the next arrives.
When data is acquired sample-by-sample while processing a frame at a time,
however, an interrupted system wastes processor instruction cycles. For example,
a system with a 200-ns interrupt response time running a frame-based algorithm,
such as the FFT, with a frame size of 1024 samples, would require 204.8 µs of
overhead. That amounts to more than 10,000 instruction cycles wasted to
latency productive time when the DSP could be performing signal processing.
This waste is easy to avoid in DSPs having architectural features such as DMA
and dual memory access; they let the DSP receive and store data without
interrupting the processor. DEVELOPING A DSP
SYSTEM
Having discussed the role of the processor, the ADC, the
anti-aliasing filter, and the timing relationships between these components, it
is time to look at a complete DSP system. Figure 8 shows the building blocks of
a typical DSP system that could be used for data acquisition and control.
Figure 8. Putting together elements of a DSP system.
Note how few components make up the DSP system, because so much of the system’s functionality comes from the programmable DSP. Converters funnel data into and out of the DSP; the ADC timing is controlled by a precise sampling clock. To simplify system design, many converter devices available today combine some or all of the following: an A/D converter, a D/A converter, a sampling clock, and filters for anti-aliasing and anti-imaging. The clock oscillator in these types of I/O components is separately controlled by an external crystal. Here are some important points about the data flow in this sort of DSP system:
Analog Input: The analog signal is appropriately band-limited by the anti-aliasing filter and applied to the input of the ADC. At the selected sampling time, the converter interrupts the DSP processor and makes the digital sample available. The choice between serial and parallel interfacing between the ADC and DSP depends on the amount of data, design complexity trade-offs, space, power, and price.
Digital Signal Processing: The incoming data is handled by the DSP’s algorithm software. When the processor completes the required calculations, it sends the result to the DAC. Because the signal processing is programmable, considerable flexibility is available in handling the data and improving system performance with incremental programming adjustments.
Analog Output: The DAC converts the DSP’s output into the desired analog output at the next sample clock. The converter’s output is smoothed by a low-pass, anti-imaging filter (also called a reconstruction filter), to produce the reconstructed analog signal.
Host Interface: An optional host interface lets the DSP communicate
with external systems, sending and receiving data and control information. REVIEW AND PREVIEW
The goal of this article has
been to provide an overview of major DSP design concepts and explain some of the
reasons why a DSP is better suited that analog circuitry for some applications.
The issues introduced in this article include:
Because these issues involve many valuable levels of detail that we could not do justice to in this brief article, you should consider reading Richard Higgins’s text, Digital Signal Processing in VLSI (see References below). This text provides a complete overview of DSP theory, implementation issues, and reduction to practice (with devices available at the time it was published), plus exercises and examples. The Reference section below also contains other sources that further amplify this article’s issues. To prepare for the next articles in this series, you might want to get free copies of the ADSP-2100 Family User’s Manual* and the ADSP-2106x SHARC User’s Manual.* These texts provide information on Analog Devices’s fixed- and floating-point DSP architectures, a major topic in these articles. The next article will cover the following territory:
Mar, A., ed. Digital Signal Processing Applications Using the ADSP-2100 Family Volume 1, Englewood Cliffs, NJ: Prentice Hall, 1992. Available for purchase from ADI.
Mar, A., Babst, J., eds. Digital Signal Processing Applications Using the ADSP-2100 Family Volume 2, Englewood Cliffs, NJ: Prentice Hall, 1994. Available for purchase from ADI.
Dearborn, G., ed. Digital Signal Processing Applications Using the ADSP-21000 Family Volume 1, Norwood, MA: Analog Devices, Inc., 1994. Available for purchase from ADI.
*Mar, A., Rempel, H., eds. ADSP-2100 Family User’s Manual, Norwood, MA: Analog Devices, Inc., 1995. Free.
Mar, A., Rempel, H., eds. ADSP-21020 Family User’s Manual, Norwood, MA: Analog Devices, Inc., 1995. Free.
*Rempel, H., ed. ADSP-21060/62 SHARC User’s Manual, Norwood, MA: Analog Devices, Inc., 1995. Free.
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