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121 lessons in eleven parts, from what a signal is to radar. Read them in any order: a prerequisite is a link, never a gate.

New here · the first lesson

What a signal is

See what a signal really is, with five small examples you can drag, toggle and step through yourself.

Start with 1.1

Contents

Part I

Signals

Chapters 1–3 · 10 lessons

Chapter 1What a signal is

  1. 1.1What a signal is , essential
  2. 1.2Kinds of signals , essential
  3. 1.3How big is a signal , essential

Chapter 2Working with signals

  1. 2.1Shifting, reversing and scaling time , essential
  2. 2.2Operations on amplitude , essential
  3. 2.3Decomposing signals , essential

Chapter 3The elementary signals

  1. 3.1Impulse, step and ramp , essential
  2. 3.2Sinusoids , essential
  3. 3.3Complex numbers for signals , essential
  4. 3.4Complex exponentials & phasors , essential
Part II

Systems

Chapters 4–6 · 9 lessons

Chapter 4Systems and their properties

  1. 4.1What is a system? , essential
  2. 4.2System properties , essential

Chapter 5LTI systems and convolution

  1. 5.1The impulse response , essential
  2. 5.2Discrete convolution , essential
  3. 5.3Continuous-time convolution , essential
  4. 5.4Properties of LTI systems , essential

Chapter 6Systems described by equations

  1. 6.1Difference equations , essential
  2. 6.2Differential equations and analog systems
  3. 6.3First- and second-order systems , essential
Part III

Fourier analysis of continuous-time signals

Chapters 7–9 · 11 lessons

Chapter 7Fourier series

  1. 7.1Signals as sums of sinusoids , essential
  2. 7.2Fourier series coefficients , essential
  3. 7.3Convergence and the Gibbs phenomenon
  4. 7.4Fourier series and LTI systems

Chapter 8The Fourier transform

  1. 8.1From series to transform , essential
  2. 8.2Properties of the Fourier transform , essential
  3. 8.3Transforms of common signals , essential
  4. 8.4Frequency response and Bode plots , essential

Chapter 9The Laplace transform

  1. 9.1The Laplace transform
  2. 9.2Properties and the inverse Laplace transform
  3. 9.3Poles, zeros and the s-plane , essential
Part IV

From analog to digital

Chapters 10–11 · 8 lessons

Chapter 10Sampling and reconstruction

  1. 10.1Sampling & aliasing , essential
  2. 10.2The sampling theorem , essential
  3. 10.3Reconstruction , essential
  4. 10.4Anti-aliasing and practical converters , essential
  5. 10.5Bandpass sampling

Chapter 11Quantization

  1. 11.1Quantization & noise , essential
  2. 11.2Dither
  3. 11.3Oversampling and noise shaping
Part V

Discrete-time Fourier analysis

Chapters 12–15 · 20 lessons

Chapter 12The discrete-time Fourier transform

  1. 12.1Frequency in discrete time , essential
  2. 12.2The DTFT , essential
  3. 12.3Properties of the DTFT , essential
  4. 12.4Frequency response of discrete-time systems , essential

Chapter 13The discrete Fourier transform

  1. 13.1Sampling the spectrum , essential
  2. 13.2The DFT , essential
  3. 13.3Properties of the DFT , essential
  4. 13.4Circular vs linear convolution , essential
  5. 13.5The DFT as a matrix
  6. 13.6The discrete cosine transform

Chapter 14The fast Fourier transform

  1. 14.1The FFT , essential
  2. 14.2More FFT algorithms
  3. 14.3Fast convolution , essential
  4. 14.4Goertzel and the chirp z-transform

Chapter 15Spectral analysis in practice

  1. 15.1Windowing & spectral leakage , essential
  2. 15.2Window functions compared , essential
  3. 15.3Zero-padding and resolution , essential
  4. 15.4Reading a spectrum: scaling and units , essential
  5. 15.5Spectrograms & the STFT , essential
  6. 15.6Inverting the STFT
Part VI

The z-transform and system analysis

Chapters 16–17 · 9 lessons

Chapter 16The z-transform

  1. 16.1The z-transform , essential
  2. 16.2Properties and the inverse z-transform , essential
  3. 16.3Transfer functions, poles & zeros , essential
  4. 16.4Stability and causality , essential
  5. 16.5The unilateral z-transform

Chapter 17Special classes of systems

  1. 17.1All-pass systems
  2. 17.2Minimum phase
  3. 17.3Linear-phase systems , essential
  4. 17.4Resonators, notches and combs , essential
Part VII

Filter design

Chapters 18–21 · 16 lessons

Chapter 18Filter fundamentals

  1. 18.1Filter specifications , essential
  2. 18.2Simple smoothing filters , essential

Chapter 19FIR filter design

  1. 19.1Window-method FIR design , essential
  2. 19.2Frequency-sampling design
  3. 19.3Optimal FIR design
  4. 19.4Special FIR filters

Chapter 20IIR filter design

  1. 20.1Analog prototype filters , essential
  2. 20.2IIR design by the bilinear transform , essential
  3. 20.3Impulse invariance
  4. 20.4Frequency transformations
  5. 20.5Audio equalisers and biquads
  6. 20.6Choosing FIR or IIR , essential

Chapter 21Implementing filters

  1. 21.1Filter structures , essential
  2. 21.2Second-order sections , essential
  3. 21.3Finite word-length effects
  4. 21.4Real-time processing
Part VIII

Multirate signal processing

Chapters 22–23 · 6 lessons

Chapter 22Changing the sample rate

  1. 22.1Downsampling and decimation , essential
  2. 22.2Upsampling and interpolation , essential
  3. 22.3Resampling by any factor
  4. 22.4Polyphase structures

Chapter 23Filter banks and wavelets

  1. 23.1Filter banks
  2. 23.2Wavelets
Part IX

Random signals and statistical signal processing

Chapters 24–26 · 12 lessons

Chapter 24Random signals

  1. 24.1Random variables for signals , essential
  2. 24.2Random processes , essential
  3. 24.3Correlation , essential
  4. 24.4Power spectral density , essential

Chapter 25Spectral estimation

  1. 25.1The periodogram , essential
  2. 25.2Averaged periodograms: Bartlett and Welch , essential
  3. 25.3Parametric models and linear prediction
  4. 25.4High-resolution frequency estimation

Chapter 26Optimal and adaptive filtering

  1. 26.1Matched filters and detection , essential
  2. 26.2The Wiener filter
  3. 26.3Adaptive filters: LMS
  4. 26.4RLS and the Kalman filter
Part X

Modulation, analytic signals and images

Chapters 27–28 · 9 lessons

Chapter 27Modulation

  1. 27.1Amplitude modulation , essential
  2. 27.2The Hilbert transform and the analytic signal
  3. 27.3I/Q and complex baseband
  4. 27.4Frequency and phase modulation
  5. 27.5Digital modulation and OFDM

Chapter 28Images as two-dimensional signals

  1. 28.1Images as signals
  2. 28.2Image filtering
  3. 28.3The 2-D DFT
  4. 28.4Image compression
Part XI

Applications

Chapters 29–33 · 11 lessons

Chapter 29Audio and music

  1. 29.1Pitch detection
  2. 29.2Audio effects
  3. 29.3Perceptual audio coding

Chapter 30Speech

  1. 30.1The source–filter model of speech
  2. 30.2Speech features

Chapter 31Biomedical signals

  1. 31.1ECG processing
  2. 31.2EEG and rhythms

Chapter 32Measurement and sensing

  1. 32.1Vibration and machine monitoring
  2. 32.2Sensor signal conditioning

Chapter 33Radar and communications

  1. 33.1Radar signal processing
  2. 33.2Channels and equalisation

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