The Scientist and Engineer's Guide to Digital Signal Processing

Citation

Smith, S. W. (1997). The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing. Free official edition: https://www.dspguide.com/pdfbook.htm

Chapter Summary

Chapter 1: The Breadth and Depth of DSP

The opening chapter states the book's premise: most practical DSP techniques can be learned and used without heavy mathematics, and the book is written for readers who want DSP as a tool rather than a career. It sketches the roots of the field and surveys application areas—telephone multiplexing, compression and echo control, audio and speech, radar, sonar and reflection seismology, and image processing in medicine (CT, MRI), space and commercial products—to show how interdisciplinary DSP is.

Chapter 2: Statistics, Probability and Noise

This chapter introduces signal terminology and the statistics used to describe acquired signals: mean, standard deviation and signal-to-noise ratio, the histogram, probability mass and density functions, and the normal distribution. It shows how to generate digital noise with a chosen distribution and closes by distinguishing precision from accuracy in measurements.

Chapter 3: ADC and DAC

Framed as information management, the chapter treats sampling and quantization as the two ways digitization limits information. It explains quantization noise, the sampling theorem and aliasing, digital-to-analog conversion with its zero-order hold, and the analog antialias and reconstruction filters needed around a converter, comparing Bessel, Butterworth and Chebyshev designs. Multirate and single-bit (delta-modulation) conversion end the chapter.

Chapter 4: DSP Software

Here the author looks at how numbers are stored in computers—fixed-point formats and floating point—and what that means for round-off error and precision, with short BASIC programs that show errors accumulating. Sections on execution speed compare programming languages, hardware and programming tips for making DSP code run faster.

Chapters 5–7: Linear Systems; Convolution; Properties of Convolution

These three chapters lay the foundation of the book. Chapter 5 defines linearity (homogeneity and additivity, plus shift invariance), gives examples of linear and nonlinear systems, and presents superposition with impulse, step, even/odd, interlaced and Fourier decompositions. Chapter 6 introduces the delta function and impulse response and explains convolution from both the input-side and output-side viewpoints, with programs for each. Chapter 7 covers common impulse responses (calculus-like operations, low-pass and high-pass kernels), causal and linear-phase signals, the commutative, associative and distributive properties for cascaded and parallel systems, the central limit theorem, and correlation as a way to detect a known waveform, for example in radar.

Chapters 8–9: The Discrete Fourier Transform; Applications of the DFT

Chapter 8 places the DFT in the family of Fourier transforms, then develops the real DFT: notation, basis functions, synthesis (inverse DFT) and analysis by simultaneous equations or by correlation, duality, and conversion to polar form with a list of practical "nuisances" in phase calculations. Chapter 9 shows the three main uses of the DFT: spectral analysis of signals (including windowing and frequency resolution), finding a system's frequency response from its impulse response, and convolution via the frequency domain.

Chapters 10–11: Fourier Transform Properties; Fourier Transform Pairs

Chapter 10 explains how operations in one domain appear in the other—linearity, the behaviour of phase under shifting, the periodic nature of the DFT, compression and expansion with multirate methods, multiplying signals (amplitude modulation) and Parseval's relation. Chapter 11 catalogues standard transform pairs: the delta function, rectangular pulse and sinc function, other common pairs, the Gibbs effect, harmonics of periodic signals, and chirp signals.

Chapter 12: The Fast Fourier Transform

The FFT chapter first shows how the real DFT can be computed with a complex DFT, then explains how the FFT works through bit-reversal sorting, the decomposition into two-point spectra and the butterfly calculation. It provides FFT programs, compares their speed and precision with the correlation-based DFT, and describes further speed-ups such as the real FFT.

Chapter 13: Continuous Signal Processing

This chapter shows that continuous-time signal processing parallels DSP, using equations and calculus instead of programs. It covers the continuous delta function and convolution, the Fourier transform and the Fourier series, with worked examples rather than code.

Chapters 14–16: Introduction to Digital Filters; Moving Average Filters; Windowed-Sinc Filters

Chapter 14 introduces filter parameters in the time and frequency domains and makes a key distinction: whether information is encoded in the time domain (where step response matters) or the frequency domain (where frequency response matters). It explains spectral inversion and reversal for building high-pass, band-pass and band-reject filters, and classifies filters by use and by implementation (convolution or recursion). Chapter 15 shows that the moving average is optimal for reducing random noise while keeping a sharp step, but poor at separating frequencies, and covers its relatives and a recursive implementation. Chapter 16 develops the windowed-sinc filter for separating frequency bands, using Blackman and Hamming windows, with examples including the separation of EEG alpha and beta waves.

Chapters 17–18: Custom Filters; FFT Convolution

Chapter 17 presents a general method for designing filters with an arbitrary frequency response and applies it to deconvolution (restoring a signal blurred by a detector, illustrated with gamma-ray pulses) and to optimal filtering, comparing the moving average, matched filter and Wiener filter. Chapter 18 explains the overlap-add method for processing long signals in segments and FFT convolution, which becomes faster than direct convolution for long filter kernels.

Chapters 19–21: Recursive Filters; Chebyshev Filters; Filter Comparison

Chapter 19 introduces recursive (IIR) filters, single-pole low-pass and high-pass designs, narrow-band filters, phase response (zero, linear and nonlinear phase, including bidirectional filtering) and integer implementations. Chapter 20 gives a practical, table- and program-based approach to Chebyshev and Butterworth recursive filters, with notes on overshoot and stability, leaving the underlying z-transform to Chapter 33. Chapter 21 stages "head-to-head" comparisons: an analog filter against a digital one, the windowed-sinc against the Chebyshev in the frequency domain, and the moving average against the single-pole filter in the time domain.

Chapter 22: Audio Processing

The audio chapter begins with human hearing, loudness and timbre, then covers high-fidelity audio and the compact disc, companding for telephone voice, speech synthesis and recognition, and nonlinear audio processing, including homomorphic methods for separating signals that have been multiplied or convolved.

Chapters 23–25: Image Formation & Display; Linear Image Processing; Special Imaging Techniques

Chapter 23 describes the structure of digital images, cameras and the eye, television video signals, other acquisition and display systems, brightness and contrast, grayscale transforms and warping. Chapter 24 applies convolution and Fourier analysis to images: point spread functions, edge enhancement, separable kernels, illumination flattening with a large kernel, Fourier image analysis and FFT convolution, with timing comparisons. Chapter 25 treats spatial resolution, signal-to-noise ratio in images, morphological processing of binary images, and computed tomography.

Chapters 26–27: Neural Networks (and more!); Data Compression

Chapter 26 contrasts algorithm-based DSP with parameter-heavy neural networks: it covers target detection and ROC curves, network architecture, training and evaluation on a letter-recognition example, and the use of the same iterative ideas to design recursive filters. Chapter 27 surveys data compression: run-length, Huffman, delta and LZW encoding, and transform compression in JPEG and MPEG.

Chapters 28–29: Digital Signal Processors; Getting Started with DSPs

These two chapters move from algorithms to hardware. Chapter 28 explains how digital signal processors differ from general microprocessors (circular buffering, Harvard-style architecture), compares fixed and floating point, C and assembly, and describes the DSP market. Chapter 29 walks through the Analog Devices SHARC family and an evaluation kit, with a design example of an FIR audio filter and a further look at fixed versus floating point.

Chapters 30–31: Complex Numbers; The Complex Fourier Transform

Chapter 30 introduces complex numbers, polar notation and their use by substitution to represent sinusoids, systems and electrical circuits. Chapter 31 develops the complex DFT, shows its mathematical equivalence to physical signals with negative frequencies, presents the complete family of Fourier transforms in complex form, and explains why the complex transform is used.

Chapters 32–33: The Laplace Transform; The z-Transform

Chapter 32 explains the s-domain, the strategy of the Laplace transform, the analysis of electric circuits, the importance of poles and zeros, and analog filter design in the s-plane (Butterworth, Chebyshev, elliptic). Chapter 33 develops the z-transform as the digital counterpart, analyses recursive systems, cascade and parallel stages, spectral inversion and gain changes, and derives the Chebyshev-Butterworth design used in Chapter 20 by placing poles in the s-plane and converting to the z-plane, closing with reflections on the best and worst of DSP.

Chapter 34: Explaining Benford's Law

The final chapter applies signal processing to a signal whose independent variable is the number line. It recounts Benford's observation about leading digits, uses homomorphic processing and a "ones scaling test" to write Benford's law as a convolution, states a compliance theorem, and analyses the log-normal distribution as an example of when data follow the law.

Key Concepts

Chapter 1: The Breadth and Depth of DSP

• DSP as a tool: the book's stance that most practical techniques can be used without the full mathematical theory.
• Interdisciplinary breadth: each application area (telecommunications, audio, sonar, imaging) has developed its own specialised DSP techniques.

Chapter 2: Statistics, Probability and Noise

• Mean and standard deviation: the basic measures of a signal's level and fluctuation, used to define signal-to-noise ratio.
• Probability density function: the continuous counterpart of the histogram, describing how likely each amplitude is.
• Precision versus accuracy: random error (spread) versus systematic error (offset from the true value).

Chapter 3: ADC and DAC

• Quantization noise: the error introduced by rounding samples to discrete levels, modelled as added noise.
• Sampling theorem: a signal can be reconstructed if sampled at more than twice its highest frequency; otherwise aliasing occurs.
• Antialias and reconstruction filters: analog filters placed before the ADC and after the DAC to limit bandwidth.

Chapter 4: DSP Software

• Fixed versus floating point: integer formats with limited range versus formats trading precision for range.
• Round-off error: errors that accumulate when finite-precision numbers are combined repeatedly.

Chapters 5–7: Linear Systems; Convolution; Properties of Convolution

• Superposition: breaking a signal into simple components, processing each, and adding the results, valid only for linear systems.
• Impulse response and convolution: a linear system is fully described by its response to a delta function, and its output is the input convolved with that response.
• Correlation: a convolution-like operation that detects a known waveform in a noisy signal.

Chapters 8–9: The Discrete Fourier Transform; Applications of the DFT

• Real DFT: decomposition of N samples into N/2 + 1 cosine and sine amplitudes.
• Frequency response: the DFT of a system's impulse response, which multiplies the input spectrum.
• Polar form: representing each frequency by magnitude and phase instead of real and imaginary parts.

Chapters 10–11: Fourier Transform Properties; Fourier Transform Pairs

• Linear phase and time shift: shifting a signal adds phase proportional to frequency.
• Rectangular pulse and sinc: a basic transform pair, with duality making the reverse also true.
• Gibbs effect: overshoot near a discontinuity when a signal is rebuilt from a finite number of sinusoids.

Chapter 12: The Fast Fourier Transform

• FFT: an algorithm that computes the DFT in about N log₂N operations instead of N².
• Butterfly: the elementary two-point calculation repeated at each stage of the FFT.

Chapter 13: Continuous Signal Processing

• Continuous convolution and Fourier transform: the calculus-based counterparts of the discrete operations.
• Fourier series: the representation of a periodic continuous signal as a sum of harmonics.

Chapters 14–16: Introduction to Digital Filters; Moving Average Filters; Windowed-Sinc Filters

• Time-domain versus frequency-domain encoding: whether a filter should be judged by its step response or its frequency response.
• Moving average filter: the optimal filter for reducing white noise while keeping a sharp step response.
• Windowed-sinc filter: a truncated, windowed sinc kernel that gives excellent separation of frequency bands.

Chapters 17–18: Custom Filters; FFT Convolution

• Deconvolution: designing a filter to undo an unwanted convolution, such as detector blurring.
• Wiener filter: an optimal filter for separating signals whose spectra overlap, based on signal and noise spectra.
• Overlap-add: splitting a long signal into segments, filtering each and adding the overlapping outputs.

Chapters 19–21: Recursive Filters; Chebyshev Filters; Filter Comparison

• Recursive (IIR) filter: a filter that uses previous outputs as well as inputs, giving a long impulse response cheaply.
• Chebyshev response: a faster roll-off obtained by allowing ripple in the passband.
• Bidirectional filtering: running a recursive filter forwards and backwards to obtain zero phase.

Chapter 22: Audio Processing

• Companding: compressing and expanding amplitude nonlinearly so that telephone voice can be carried with fewer bits.
• Homomorphic processing: transforming signals so that multiplied or convolved components become added and can be separated linearly.

Chapters 23–25: Image Formation & Display; Linear Image Processing; Special Imaging Techniques

• Point spread function: the image equivalent of the impulse response.
• Separable convolution: performing a 2-D convolution as row and column 1-D convolutions to save computation.
• Computed tomography: reconstructing a cross-sectional image from many projections.

Chapters 26–27: Neural Networks (and more!); Data Compression

• ROC curve: a graphical way to evaluate the trade-off between detecting targets and false alarms.
• Training a neural network: iteratively adjusting many weights to reduce error on example data.
• Transform compression: JPEG-style compression that quantizes DCT coefficients of image blocks.

Chapters 28–29: Digital Signal Processors; Getting Started with DSPs

• Circular buffering: a memory scheme that keeps the most recent samples for real-time filtering.
• DSP architecture: separate program and data memory buses that let a processor fetch an instruction and data in the same cycle.

Chapters 30–31: Complex Numbers; The Complex Fourier Transform

• Complex substitution: representing sinusoids and circuit elements with complex numbers to simplify calculation.
• Negative frequencies: the complex DFT's representation of real signals as pairs of positive and negative frequency components.

Chapters 32–33: The Laplace Transform; The z-Transform

• Poles and zeros: the points in the s-plane or z-plane that determine a system's frequency response.
• z-transform: the discrete-time counterpart of the Laplace transform, used to design recursive filters.

Chapter 34: Explaining Benford's Law

• Benford's law: the observation that leading digits in many data sets are not uniformly distributed.
• Ones scaling test: a signal-processing view of when a distribution follows Benford's law.

Critical Analysis

Strengths

• Practical orientation stated and kept. The author's premise in Chapter 1 is that DSP can be used as a tool without the traditional mathematical barriers, and the book follows through: the real DFT is introduced before complex numbers, filters are designed with tables and programs, and the Laplace and z-transforms are deferred to the end.
• Clear criteria for choosing methods. The distinction in Chapter 14 between time-domain and frequency-domain encoded information gives readers a practical rule for choosing filters, and Chapter 21's comparisons (analog versus digital, windowed-sinc versus Chebyshev, moving average versus single pole) turn that rule into concrete decisions.
• Programs and figures throughout. Short programs show each algorithm (convolution, the DFT by correlation, the FFT, filter design), and almost every idea is illustrated with a figure, which makes the book readable for scientists outside electrical engineering.
• Broad applied coverage. Beyond filters and transforms, the book covers converters, audio, images, computed tomography, compression, neural networks and DSP hardware, with biomedical examples such as fetal EKG, EEG alpha and beta waves, and CT.

Limitations

• Dated technology and code. Programs are written in an old line-numbered BASIC style, and the hardware chapters describe late-1990s products such as the SHARC EZ-KIT Lite and market data of that period. The concepts remain valid, but readers will translate the code into Python or MATLAB.
• No exercises. The chapters contain no problem sets or worked solutions, so a course must supply its own assignments.
• Light on rigour in places. The deliberate avoidance of mathematics means topics such as stochastic processes, spectral estimation theory, adaptive filtering and multirate filter banks receive little or no treatment, and statistical derivations are informal.
• Format of the free edition. The book is distributed as 34 separate chapter PDFs; on the current site the chapter list page did not display its table of contents, and no front matter (preface or index) is linked, so readers navigate by chapter number.

Applications in the Book

Applications are concentrated in the second half: audio processing (Chapter 22: hearing, compact disc, telephone companding, speech synthesis and recognition), image formation, linear image processing and special imaging techniques including computed tomography (Chapters 23–25), neural networks for target detection and letter recognition (Chapter 26), data compression including JPEG and MPEG (Chapter 27), and DSP hardware with an FIR audio filter design example (Chapters 28–29). Chapter 1 surveys applications in telecommunications, radar, sonar, seismology and medical imaging, and examples such as EKG noise removal, EEG band separation and gamma-ray deconvolution appear within the filter chapters.

Where It Fits in the Course

In the Biomedical Signal Processing list, Smith's guide is a broad, gentle introduction to DSP itself. Semmlow's Circuits, Signals, and Systems for Bioengineers is also an introductory text and, by its description, teaches signals and systems with MATLAB in a bioengineering setting; Smith complements it with intuitive coverage of convolution, the DFT and digital filter design, and it can be read before or alongside it. Semmlow and Griffel's Biosignal and Medical Image Processing is the natural next step for biomedical-specific methods applied to physiological signals and medical images.

Rangayyan's Biomedical Signal Analysis and Tompkins's Biomedical Digital Signal Processing are specialist biomedical texts; Tompkins is described as a C-language laboratory text for the PC. Smith's Chapters 5–21 supply the filtering and Fourier background those books assume, while Chapters 22–29 broaden the view to audio, imaging and hardware. Smith should be read before, not instead of, the specialist biomedical texts.

How to Use This Book

The book is aimed at scientists and engineers who need to use DSP; algebra and basic programming are enough for most chapters, and calculus is needed only for Chapter 13 and the complex-domain chapters. A core path for a biomedical signal-processing course is Chapters 1–3, 5–12 and 14–21; Chapter 4 can be skimmed, and Chapter 13 read for the link to continuous-time theory. Chapters 22–25 and 27 are optional depending on whether audio, imaging or compression matters for the course, and Chapters 28–29 are relevant only to hardware projects. Chapters 30–33 form a self-contained advanced section for students who will go on to Laplace and z-domain filter design.

Because there are no exercises, re-implement each program in a modern language as you read—convolution, the DFT by correlation, a moving average, a windowed-sinc filter and a single-pole recursive filter—and test them on real physiological recordings. Check the site's errata page while reading.

Edition and Sources

This guide is based on the free chapter PDFs (Chapters 1–34) posted on the author's official site, https://www.dspguide.com/pdfbook.htm (individual files at dspguide.com/CH1.PDF to CH34.PDF), together with the site's notes on editions and permitted use; the hardcover was published by California Technical Publishing in 1997 and a paperback by Newnes in 2002. It draws on all 34 chapters: each chapter introduction, every section heading, the central figures, tables and programs, and the closing sections of the filter and transform chapters.