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Contents

Signals

What a signal is

  1. What a signal is , essential
  2. Kinds of signals , essential
  3. How big is a signal , essential

Working with signals

  1. Shifting, reversing and scaling time , essential
  2. Operations on amplitude , essential
  3. Decomposing signals , essential

The elementary signals

  1. Impulse, step and ramp , essential
  2. Sinusoids , essential
  3. Complex numbers for signals , essential
  4. Complex exponentials and phasors , essential

Systems

Systems and their properties

  1. What is a system? , essential
  2. System properties , essential

LTI systems and convolution

  1. The impulse response , essential
  2. Discrete convolution , essential
  3. Continuous-time convolution , essential
  4. Properties of LTI systems , essential

Systems described by equations

  1. Difference equations , essential
  2. Differential equations and analog systems
  3. First- and second-order systems , essential

Fourier analysis

Fourier series

  1. Signals as sums of sinusoids , essential
  2. Fourier series coefficients , essential
  3. Convergence and the Gibbs phenomenon
  4. Fourier series and LTI systems

The Fourier transform

  1. From series to transform , essential
  2. Properties of the Fourier transform , essential
  3. Transforms of common signals , essential
  4. Frequency response and Bode plots , essential

The Laplace transform

  1. The Laplace transform
  2. Properties and the inverse Laplace transform
  3. Poles, zeros and the s-plane , essential

Analog to digital

Sampling and reconstruction

  1. Sampling and aliasing , essential
  2. The sampling theorem , essential
  3. Reconstruction , essential
  4. Anti-aliasing and practical converters , essential
  5. Bandpass sampling

Quantization

  1. Quantization and noise , essential
  2. Dither
  3. Oversampling and noise shaping

Discrete-time Fourier analysis

The discrete-time Fourier transform

  1. Frequency in discrete time , essential
  2. The DTFT , essential
  3. Properties of the DTFT , essential
  4. Frequency response of discrete-time systems , essential

The discrete Fourier transform

  1. Sampling the spectrum , essential
  2. The DFT , essential
  3. Properties of the DFT , essential
  4. Circular vs linear convolution , essential
  5. The DFT as a matrix
  6. The discrete cosine transform

The fast Fourier transform

  1. The FFT , essential
  2. More FFT algorithms
  3. Fast convolution , essential
  4. Goertzel and the chirp z-transform

Spectral analysis in practice

  1. Windowing and spectral leakage , essential
  2. Window functions compared , essential
  3. Zero-padding and resolution , essential
  4. Reading a spectrum: scaling and units , essential
  5. Spectrograms and the STFT , essential
  6. Inverting the STFT

The z-transform

The z-transform

  1. The z-transform , essential
  2. Properties and the inverse z-transform , essential
  3. Transfer functions, poles and zeros , essential
  4. Stability and causality , essential
  5. The unilateral z-transform

Special classes of systems

  1. All-pass systems
  2. Minimum phase
  3. Linear-phase systems , essential
  4. Resonators, notches and combs , essential

Filter design

Filter fundamentals

  1. Filter specifications , essential
  2. Simple smoothing filters , essential

Implementing filters

  1. Filter structures , essential
  2. Second-order sections , essential
  3. Finite word-length effects
  4. Real-time processing

FIR filter design

  1. Window-method FIR design , essential
  2. Frequency-sampling design
  3. Optimal FIR design
  4. Special FIR filters

IIR filter design

  1. Analog prototype filters , essential
  2. IIR design by the bilinear transform , essential
  3. Impulse invariance
  4. Frequency transformations
  5. Audio equalisers and biquads
  6. Choosing FIR or IIR , essential

Multirate processing

Changing the sample rate

  1. Downsampling and decimation , essential
  2. Upsampling and interpolation , essential
  3. Resampling by any factor
  4. Polyphase structures

Filter banks and wavelets

  1. Filter banks
  2. Wavelets

Random signals

Random signals

  1. Random variables for signals , essential
  2. Random processes , essential
  3. Correlation , essential
  4. Power spectral density , essential

Spectral estimation

  1. The periodogram , essential
  2. Averaged periodograms: Bartlett and Welch , essential
  3. Parametric models and linear prediction
  4. High-resolution frequency estimation

Optimal and adaptive filtering

  1. Matched filters and detection , essential
  2. The Wiener filter
  3. Adaptive filters: LMS
  4. RLS and the Kalman filter

Modulation and images

Modulation

  1. Amplitude modulation , essential
  2. The Hilbert transform and the analytic signal
  3. I/Q and complex baseband
  4. Frequency and phase modulation
  5. Digital modulation and OFDM

Images as two-dimensional signals

  1. Images as signals
  2. Image filtering
  3. The 2-D DFT
  4. Image compression

Applications

Audio and music

  1. Pitch detection
  2. Audio effects
  3. Perceptual audio coding

Speech

  1. The source–filter model of speech
  2. Speech features

Measurement and sensing

  1. Vibration and machine monitoring
  2. Sensor signal conditioning

Biomedical signals

  1. ECG processing
  2. EEG and rhythms

Radar and communications

  1. Radar signal processing
  2. Channels and equalisation

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Signal processing
Linear algebra
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