Utah State University
Department of Electrical and Computer Engineering
ECE 3640 - Discrete-time Signals & Systems

Resources

Textbook Coverage in ECE 3640 (Chapters 2-5, 7, 8, 10)

We have an excellent textbook for this class. However, the authors present the topics in the wrong order. We will cover the textbook chapters in the order given below.

Mathematical preliminaries (should be review, see links below)
Discrete-time signals in the time domain (extension of continuous-time signals ideas) [Holton 1]
Discrete-time systems in the time domain (convolution, impulse response, filtering) [Holton 2]
Discrete-time Fourier transform (DTFT) [Holton 3]
Sampling and reconstruction [Holton 6]
Discrete Fourier transform (DFT) [Holton 10]
Signal analysis [Holton 14]
Z-transform (ZT) [Holton 4]
System analysis and design [Holton 5, 7, 8] (FIR filter design video lecture)

Dr. Gunther's YouTube Channel

Slide Sets and Videos

Lecture video page may be accessed here
What is digital signal processing?
Discrete-time signals in the time domain
- Slides
- Video: Discrete-Time Signals: Definition and Examples [22 min. @ 1.5x]
- Video: Discrete-Time Signals: Operations and Common Signals [24 min. @ 1.5x]
- Video: Discrete-Time Signals: Classification and Decompositions [12 min. @ 1.5x]
- dolphin1.wav
- whale1.wav
- whale2.wav
- sonar1.wav
- fireflyintro1.wav
- fireflyintro1_slow.wav
- Follow up questions
Mathematical preliminaries
- Exponential integral Slides Video [15 min. @ 1.5x]
- Exponential sum Slides Video [21 min. @ 1.5x]
- Complex exponential signals Slides Video [33 min. @ 1.5x]
Introduction to discrete-time signals and systems (old stuff)
Notes on discrete-time systems in the time domain Slides Video
Notes on impulse response for discrete-time LTI systems Slides
Notes on the mechanics of convolution Slides, Picture, Spreadsheet
- Convolution as matrix-vector product
- Transient outputs, valid outputs
- Tableau method
- Summary slide
- 3Blue1Brown Convolution YouTube Video
Cascades of LTI systems Slides
Origin of convolution
- speech input
- speech output
LTI system topics
- Mechanics of FIR filtering
- Mechanics of IIR filtering
- LTI systems - Part 1
- LTI systems - Part 2
LTI Difference Equations Slides
Notes on the DTFT (PDF) (Keynote) (Frequency Sweep GIF)
Notes on the DTFT (old stuff)
$u[n]$ video
DTFT: Things to know and do
Notes on sampling and reconstruction
Notes on sample rate conversion
$z$ -transform
$z$ -transform (old stuff)
Notes on acoustic reverberation
$z$ -transform
Notes on windowed FIR filter design

Topics in Markdown

Matlab Scripts/Functions

Convolution
- financial index data
- Matlab script (illustrates startup and ending transients and valid convolution outputs)
DTFT
- window_example.m
DFT
Adjustable BPF
- System diagram
- Signals drawing
- Signals
- Audio in
- Audio out (500 to 2000 Hz pass band)
Sampling
$Z$ -transform analysis of LTI systems
FIR filter design

Signal Processing Links

IEEE Signal Processing Society YouTube Channel

IEEE Signal Processing Society

Signal processing 101

What is signal processing

Signal processing and machine learning

What are audio effects? Sound basics with Stella - Episode 1

Equalization explained. Sound basics with Stella - Episode 2

Amazing sound engineer

Digital audio effects

Computational photography

Video stabilization

C Programming

C Programming (WikiBooks)
A Little C Primer (WikiBooks)
(http://www.cprogramming.com/) (click on C tutorial in sidebar)
www.tutorialspoint.com/cprogramming (lots of links in the sidebar and a search box in the top right)
www.tutorialspoint.com/c_standard_library (all the standard C libraries)
The C Programming Language, K&R (book available through USU Library)
Complete 4 hour video course on C (video available through USU Library)
www.cplusplus.com (great site for C++, but you can search for elements of C, e.g. fread, fwrite, etc.)

Matlab

Matlab tutorial written by Dr. Todd Moon
Matlab documentation
Video tutorials by the Mathworks
Fundamentals of Signals and Systems (2 ed) by Kamen and Heck
Matlab tutorial (Many tutorials can be found on the Web. Here is one example.)

Unix/Linux

Using GCC

Fast Fourier Transform

Fastest Fourier Transform in the West (FFTW)


#include "fftw3.h” // You may need to include the full file path to this .h file
int main(void)
{
  fftw_complex *in, *out;
  fftw_plan p;
  int N = 1024;
  in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
  out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
  // Fill the in array with signal values
  p = fftw_plan_dft_1d(N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
  fftw_execute(p); /* repeat as needed */
  fftw_destroy_plan(p);
  fftw_free(in); fftw_free(out);
  return 1;
}

KISS FFT (Here is a sample program kfft_test.c)


x
#include "kiss_fft.h"

// This file is named:  kfft_test.c
// Build using command line:  gcc -o kfft_test kfft_test.c kiss_fft.c
// Run the program using command line:  ./kfft_test
// Output:
// |X[0]|^2 =    0.00000
// |X[1]|^2 =    4.00000
// |X[2]|^2 =    0.00000
// |X[3]|^2 =    4.00000
// x[0]=   1.00000+j   0.00000, y[0]=   1.00000+j   0.00000
// x[1]=   0.00000+j   0.00000, y[1]=   0.00000+j   0.00000
// x[2]=  -1.00000+j   0.00000, y[2]=  -1.00000+j   0.00000
// x[3]=   0.00000+j   0.00000, y[3]=   0.00000+j   0.00000

int main(void) {
  int k;
  // Set up buffers for FFT
  int nfft = 4;
  kiss_fft_cfg  fft = kiss_fft_alloc(nfft,0,NULL,NULL);
  kiss_fft_cfg ifft = kiss_fft_alloc(nfft,1,NULL,NULL);
  kiss_fft_cpx *x = KISS_FFT_MALLOC(nfft * sizeof(kiss_fft_cpx));
  kiss_fft_cpx *X = KISS_FFT_MALLOC(nfft * sizeof(kiss_fft_cpx));
  kiss_fft_cpx *y = KISS_FFT_MALLOC(nfft * sizeof(kiss_fft_cpx));
  kiss_fft_cpx *Y = KISS_FFT_MALLOC(nfft * sizeof(kiss_fft_cpx));
  // Fill up the real and imaginary parts of the input signal
  x[0].r =  1.0; x[0].i = 0.0;
  x[1].r =  0.0; x[1].i = 0.0;
  x[2].r = -1.0; x[2].i = 0.0;
  x[3].r =  0.0; x[3].i = 0.0;
  // Compute the FFT
  kiss_fft(fft,x,X);
  // Copy X to Y
  for(k=0; k<nfft; k++) {
    Y[k].r = X[k].r;
    Y[k].i = X[k].i;
    printf("|X[%d]|^2 = %10.5f\n",k,X[k].r*X[k].r+X[k].i*X[k].i);
  }
  // Compute the inverse FFT
  kiss_fft(ifft,Y,y);
  for(k=0; k<nfft; k++) {
    y[k].r /= nfft;
    y[k].i /= nfft;
  }
  // Print out stuff
  for(k=0; k<nfft; k++) {
    printf("x[%d]=%10.5f+j%10.5f, y[%d]=%10.5f+j%10.5f\n",                       k,x[k].r,x[k].i,k,y[k].r,y[k].i);
  }
  // Deallocate memory
  free( fft);
  free(ifft);
  kiss_fft_cleanup();
  return 1;
}

Real-Time Audio Signal Processing Using JUCE

JUCE Web Site

A Few Things to Memorize

$z$ -Transform
Mathematical principles for deriving transform properties, symmetries and pairs
Geometric sum/series formulas:

\begin{matrix} (1) & \begin{matrix} \sum_{n = N}^{M - 1} a^{n} = {\begin{cases} M - N, & a = 1, \\ \frac{a^{N} - a^{M}}{1 - a}, & a \neq 1 \end{cases} \\ \sum_{n = 0}^{\infty} a^{n} = \frac{1}{1 - a}, | a | < 1 \end{matrix} \end{matrix}

Sine construction formula:

\begin{matrix} (2) & \frac{e^{j A} - e^{- j B}}{2 j} = \frac{e^{j \frac{A + B}{2}} - e^{- j \frac{A + B}{2}}}{2 j} e^{j \frac{A - B}{2}} = \sin (\frac{A + B}{2}) e^{j \frac{A - B}{2}} \end{matrix}

Resources

Canvas

First Day

Online Books on DSP

Textbook Coverage in ECE 3640 (Chapters 2-5, 7, 8, 10)

Dr. Gunther's YouTube Channel

Slide Sets and Videos

Topics in Markdown

Matlab Scripts/Functions

Signal Processing Links

C Programming

Matlab

Unix/Linux

Using GCC

Fast Fourier Transform

Real-Time Audio Signal Processing Using JUCE

A Few Things to Memorize