DSP First, 2nd edition

  • James H. McClellan, 
  • Ronald Schafer, 
  • Mark Yoder

Your access includes:

  • Search, highlight, and take notes
  • Easily create flashcards
  • Use the app for access anywhere
  • 14-day refund guarantee

$10.99per month

4-month term, pay monthly or pay $43.96

Learn more, spend less

  • Special partners and offers

    Enjoy perks from special partners and offers for students

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

  • Easily continue access

    Keep learning with auto-renew


DSP First offers an accessible overview of digital signal processing. Authors James McClellan, Ronald Schafer and Mark Yoder proceed from the premise that signal processing is the best starting point for the study of electrical and computer engineering. They introduce the use of mathematics as the best language for thinking about engineering problems.

The 2nd Edition offers 3 new chapters, on the Fourier Series, Discrete-Time Fourier Transform, and the Discrete Fourier Transform. Other highlights include updated labs, visual demos, updates to existing chapters and hundreds of new homework problems with solutions. In addition, the text yields opportunities for hands-on experiences with MATLAB.

Published by Pearson (January 1st 2022) - Copyright © 2016

ISBN-13: 9780137848188

Subject: Electrical Engineering

Category: Digital Signals & Systems

Table of contents


1-1 Mathematical Representation of Signals  

1-2 Mathematical Representation of Systems       

1-3       Systems as Building Blocks

1-4       The Next Step


2-1       Tuning Fork Experiment   

2-2 Review of Sine and Cosine Functions

2-3Sinusoidal Signals

2-3.1Relation of Frequency to Period

2-3.2  Phase and Time Shift

2-4 Sampling and Plotting Sinusoids

2-5Complex Exponentials and Phasors

2-5.1 Review of Complex Numbers

2-5.2 Complex Exponential Signals

2-5.3  The Rotating Phasor Interpretation

2-5.4  Inverse Euler Formulas Phasor Addition

2-6Phasor Addition

2-6.1  Addition of Complex Numbers

2-6.2  Phasor Addition Rule

2-6.3  Phasor Addition Rule: Example

2-6.4  MATLAB Demo of Phasors

2-6.5  Summary of the Phasor Addition Rule Physics of the Tuning Fork

2-7.1  Equations from Laws of Physics

2-7.2  General Solution to the Differential Equation

2-7.3  Listening to Tones

2-8Time Signals: More Than Formulas

Summary and Links


Spectrum Representation  

3-1 The Spectrum of a Sum of Sinusoids

3-1.1  Notation Change

3-1.2  Graphical Plot of the Spectrum

3-1.3  Analysis vs. Synthesis

Sinusoidal Amplitude Modulation

3-2.1  Multiplication of Sinusoids

3-2.2  Beat Note Waveform

3-2.3  Amplitude Modulation

3-2.4  AM Spectrum

3-2.5  The Concept of Bandwidth

Operations on the Spectrum

3-3.1  Scaling or Adding a Constant

3-3.2  Adding Signals

3-3.3  Time-Shifting x.t/ Multiplies ak by a Complex Exponential

3-3.4  Differentiating x.t/ Multiplies ak by .j 2nfk/

3-3.5  Frequency Shifting

Periodic Waveforms

3-4.1  Synthetic Vowel

3-4.3  Example of a Non-periodic Signal

Fourier Series

3-5.1  Fourier Series: Analysis

3-5.2  Analysis of a Full-Wave Rectified Sine Wave

3-5.3  Spectrum of the FWRS Fourier Series

3-5.3.1  DC Value of Fourier Series

3-5.3.2  Finite Synthesis of a Full-Wave Rectified Sine

Time—Frequency Spectrum

3-6.1  Stepped Frequency

3-6.2  Spectrogram Analysis

Frequency Modulation: Chirp Signals

3-7.1  Chirp or Linearly Swept Frequency

3-7.2  A Closer Look at Instantaneous Frequency

Summary and Links


Fourier Series

Fourier Series Derivation

4-1.1  Fourier Integral Derivation

Examples of Fourier Analysis

4-2.1  The Pulse Wave

4-2.1.1  Spectrum of a Pulse Wave

4-2.1.2  Finite Synthesis of a Pulse Wave

4-2.2  Triangle Wave

4-2.2.1  Spectrum of a Triangle Wave

4-2.2.2  Finite Synthesis of a Triangle Wave

4-2.3  Half-Wave Rectified Sine

4-2.3.1  Finite Synthesis of a Half-Wave Rectified Sine

Operations on Fourier Series

4-3.1  Scaling or Adding a Constant

4-3.2  Adding Signals

4-3.3  Time-Scaling

4-3.4  Time-Shifting x.t/ Multiplies ak by a Complex Exponential

4-3.5  Differentiating x.t/ Multiplies ak by .j!0k/

4-3.6  Multiply x.t/ by Sinusoid

Average Power, Convergence, and Optimality

4-4.1  Derivation of Parseval’s Theorem

4-4.2  Convergence of Fourier Synthesis

4-4.3  Minimum Mean-Square Approximation

Pulsed-Doppler Radar Waveform

4-5.1  Measuring Range and Velocity


Sampling and Aliasing  


5-1.1  Sampling Sinusoidal Signals

5-1.2  The Concept of Aliasing

5-1.3  Spectrum of a Discrete-Time Signal

5-1.4  The Sampling Theorem

5-1.5  Ideal Reconstruction

Spectrum View of Sampling and Reconstruction

5-2.1  Spectrum of a Discrete-Time Signal Obtained by Sampling

5-2.2  Over-Sampling

5-2.3  Aliasing Due to Under-Sampling

5-2.4  Folding Due to Under-Sampling

5-2.5  Maximum Reconstructed Frequency

Strobe Demonstration

5-3.1  Spectrum Interpretation

Discrete-to-Continuous Conversion

5-4.1  Interpolation with Pulses

5-4.2  Zero-Order Hold Interpolation

5-4.3  Linear Interpolation

5-4.4  Cubic Spline Interpolation

5-4.5  Over-Sampling Aids Interpolation

5-4.6  Ideal Bandlimited Interpolation

The Sampling Theorem

Summary and Links


FIR Filters         

6-1 Discrete-Time Systems

6-2 The Running-Average Filter

6-3 The General FIR Filter

6-3.1  An Illustration of FIR Filtering

The Unit Impulse Response and Convolution

6-4.1  Unit Impulse Sequence

6-4.2  Unit Impulse Response Sequence

6-4.2.1  The Unit-Delay System

6-4.3  FIR Filters and Convolution

6-4.3.1  Computing the Output of a Convolution

6-4.3.2  The Length of a Convolution

6-4.3.3  Convolution in MATLAB

6-4.3.4  Polynomial Multiplication in MATLAB

6-4.3.5  Filtering the Unit-Step Signal

6-4.3.6  Convolution is Commutative

6-4.3.7  MATLAB GUI for Convolution

Implementation of FIR Filters

6-5.1  Building Blocks

6-5.1.1  Multiplier

6-5.1.2  Adder

6-5.1.3  Unit Delay

6-5.2  Block Diagrams

6-5.2.1  Other Block Diagrams

6-5.2.2  Internal Hardware Details

Linear Time-Invariant (LTI) Systems

6-6.1  Time Invariance

6-6.2  Linearity

6-6.3  The FIR Case

Convolution and LTI Systems

6-7.1  Derivation of the Convolution Sum

6-7.2  Some Properties of LTI Systems

Cascaded LTI Systems

Example of FIR Filtering

Summary and Links

Problems Frequency Response of FIR Filters

7-1 Sinusoidal Response of FIR Systems

7-2 Superposition and the Frequency Response

7-3 Steady-State and Transient Response

7-4 Properties of the Frequency Response

7-4.1  Relation to Impulse Response and Difference Equation

7-4.2  Periodicity of H.ej !O /

7-4.3  Conjugate Symmetry Graphical Representation of the Frequency Response

7-5.1  Delay System

7-5.2  First-Difference System

7-5.3  A Simple Lowpass Filter Cascaded LTI Systems

Running-Sum Filtering

7-7.1  Plotting the Frequency Response

7-7.2  Cascade of Magnitude and Phase

7-7.3  Frequency Response of Running Averager

7-7.4  Experiment: Smoothing an Image

Filtering Sampled Continuous-Time Signals

7-8.1  Example: Lowpass Averager

7-8.2  Interpretation of Delay

Summary and Links


The Discrete-Time Fourier Transform

DTFT: Discrete-Time Fourier Transform

8-1.1  The Discrete-Time Fourier Transform

8-1.1.1  DTFT of a Shifted Impulse Sequence

8-1.1.2  Linearity of the DTFT

8-1.1.3  Uniqueness of the DTFT

8-1.1.4  DTFT of a Pulse

8-1.1.5  DTFT of a Right-Sided Exponential Sequence

8-1.1.6  Existence of the DTFT

8-1.2  The Inverse DTFT

8-1.2.1  Bandlimited DTFT

8-1.2.2  Inverse DTFT for the Right-Sided Exponential

8-1.3  The DTFT is the Spectrum

Properties of the DTFT

8-2.1  The Linearity Property

8-2.2  The Time-Delay Property

8-2.3  The Frequency-Shift Property

8-2.3.1  DTFT of a Complex Exponential

8-2.3.2  DTFT of a Real Cosine Signal

8-2.4  Convolution and the DTFT

8-2.4.1  Filtering is Convolution

8-2.5  Energy Spectrum and the Autocorrelation Function

8-2.5.1  Autocorrelation Function

Ideal Filters

8-3.1  Ideal Lowpass Filter

8-3.2  Ideal Highpass Filter

8-3.3  Ideal Bandpass Filter

Practical FIR Filters

8-4.1  Windowing

8-4.2  Filter Design

8-4.2.1  Window the Ideal Impulse Response

8-4.2.2  Frequency Response of Practical Filters

8-4.2.3  Passband Defined for the Frequency Response

8-4.2.4  Stopband Defined for the Frequency Response

8-4.2.5  Transition Zone of the LPF

8-4.2.6  Summary of Filter Specifications

8-4.3  GUI for Filter Design

Table of Fourier Transform Properties and Pairs

Summary and Links


The Discrete Fourier Transform              

Discrete Fourier Transform (DFT)

9-1.1  The Inverse DFT

9-1.2  DFT Pairs from the DTFT

9-1.2.1  DFT of Shifted Impulse

9-1.2.2  DFT of Complex Exponential

9-1.3  Computing the DFT

9-1.4  Matrix Form of the DFT and IDFT

Properties of the DFT

9-2.1  DFT Periodicity for XŒk]

9-2.2  Negative Frequencies and the DFT

9-2.3  Conjugate Symmetry of the DFT

9-2.3.1  Ambiguity at XŒN=2]

9-2.4  Frequency Domain Sampling and Interpolation

9-2.5  DFT of a Real Cosine Signal

Inherent Periodicity of xŒn] in the DFT

9-3.1  DFT Periodicity for xŒn]

9-3.2  The Time Delay Property for the DFT

9-3.2.1  Zero Padding

9-3.3  The Convolution Property for the DFT

Table of Discrete Fourier Transform Properties and Pairs

Spectrum Analysis of Discrete Periodic Signals

9-5.1  Periodic Discrete-time Signal: Fourier Series

9-5.2  Sampling Bandlimited Periodic Signals

9-5.3  Spectrum Analysis of Periodic Signals


9-6.0.1  DTFT of Windows

The Spectrogram

9-7.1  An Illustrative Example

9-7.2  Time-Dependent DFT

9-7.3  The Spectrogram Display

9-7.4  Interpretation of the Spectrogram

9-7.4.1  Frequency Resolution

9-7.5  Spectrograms in MATLAB

The Fast Fourier Transform (FFT)

9-8.1  Derivation of the FFT

9-8.1.1  FFT Operation Count

Summary and Links



Definition of the z-Transform

Basic z-Transform Properties

10-2.1  Linearity Property of the z-Transform

10-2.2  Time-Delay Property of the z-Transform

10-2.3  A General z-Transform Formula

The z-Transform and Linear Systems

10-3.1  Unit-Delay System

10-3.2  z-1 Notation in Block Diagrams

10-3.3   The z-Transform of an FIR Filter

10-3.4   z-Transform of the Impulse Response

10-3.5  Roots of a z-transform Polynomial

Convolution and the z-Transform

10-4.1  Cascading Systems

10-4.2  Factoring z-Polynomials

10-4.3  Deconvolution

Relationship Between the z-Domain and the !O -Domain

10-5.1   The z-Plane and the Unit Circle

The Zeros and Poles of H.z/

10-6.1  Pole-Zero Plot

10-6.2   Significance of the Zeros of H.z/

10-6.3  Nulling Filters

10-6.4  Graphical Relation Between z and !O

10-6.5  Three-Domain Movies

Simple Filters

10-7.1   Generalize the L-Point Running-Sum Filter

10-7.2  A Complex Bandpass Filter

10-7.3  A Bandpass Filter with Real Coefficients

Practical Bandpass Filter Design

Properties of Linear-Phase Filters

10-9.1  The Linear-Phase Condition

10-9.2  Locations of the Zeros of FIR Linear-Phase Systems

Summary and Links


IIR Filters          

The General IIR Difference Equation

Time-Domain Response

11-2.1  Linearity and Time Invariance of IIR Filters

11-2.2  Impulse Response of a First-Order IIR System

11-2.3  Response to Finite-Length Inputs

11-2.4  Step Response of a First-Order Recursive System

System Function of an IIR Filter

11-3.1  The General First-Order Case

11-3.2  H.z/ from the Impulse Response

11-3.3  The z-Transform Method

The System Function and Block-Diagram Structures

11-4.1  Direct Form I Structure

11-4.2  Direct Form II Structure

11-4.3  The Transposed Form Structure

Poles and Zeros

11-5.1  Roots in MATLAB

11-5.2  Poles or Zeros at z D 0 or 1

11-5.3  Output Response from Pole Location

Stability of IIR Systems

11-6.1  The Region of Convergence and Stability

Frequency Response of an IIR Filter

11-7.1  Frequency Response using MATLAB

11-7.2  Three-Dimensional Plot of a System Function

Three Domains

The Inverse z-Transform and Some Applications

11-9.1  Revisiting the Step Response of a First-Order System

11-9.2  A General Procedure for Inverse z-Transformation

Steady-State Response and Stability

Second-Order Filters

11-11.1 z-Transform of Second-Order Filters

11-11.2 Structures for Second-Order IIR Systems

11-11.3 Poles and Zeros

11-11.4 Impulse Response of a Second-Order IIR System

11-11.4.1  Distinct Real Poles

11-11.5 Complex Poles

Frequency Response of Second-Order IIR Filter

11-12.1 Frequency Response via MATLAB

11-12.23-dB Bandwidth

11-12.3 Three-Dimensional Plot of System Functions

Example of an IIR Lowpass Filter

Summary and Links


Your questions answered

Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.

A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.

Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.

Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.

When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.

When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.

We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.