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STUDY GUIDE · GKU 7

Signal processing study guide (Computer Engineering)

Every sensor reading, audio stream and radio signal a computer handles is a sequence of numbers taken from a continuous signal. This unit first treats the systems that process such sequences: how the impulse response and the convolution sum give the output of any linear time-invariant system, how the z-transform and the Laplace transform turn difference and differential equations into algebra, how the DTFT and the DFT describe a signal by its frequencies, and how the frequency response tells what a filter does. The second part is the bridge between the analogue and the digital world: the sampling theorem and aliasing, the error added by quantisation, and the spectra of periodic and aperiodic signals. Exam questions are mostly short computations — a convolution, an inverse transform, a DFT, a gain, an alias frequency, a number of bits — so every section works them in full.

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Structured by the official ETEC subject standard for this topic: every listed topic and learning outcome, with formulas, figures and worked examples. The full sections are available to members in the app.

SKU 7.1 · Convolution and transformation

  1. Impulse response and convolution

    Why a linear time-invariant system is completely described by its impulse response, how the convolution sum computes its output for any input (by table and by flip-and-slide), and how causality and stability are read from the impulse response.

  2. The z-transform: transfer functions, poles and inverse transforms

    The z-transform and its region of convergence, the properties that turn delays into powers of and convolution into multiplication, the transfer function of a difference equation, stability from pole positions, and the inverse transform by partial fractions.

  3. The Laplace transform for continuous signals

    The Laplace transform of the common continuous-time signals, the derivative and final-value properties, the inverse transform by partial fractions, solving a differential equation with initial rest, and how the s-plane maps to the z-plane when a system is sampled.

  4. DTFT, DFT and FFT

    The discrete-time Fourier transform as the spectrum of a sequence, the DFT as samples of it that a computer can calculate, their key properties (periodicity, symmetry, Parseval, circular convolution), frequency resolution and bin frequencies, and why the FFT makes it practical.

  5. Frequency response and FIR/IIR filters

    What the frequency response means (the gain and phase a sinusoid receives), how to evaluate it from or , how pole and zero positions shape it, and how FIR and IIR filters compare, with a moving average, a first-order smoother and a mains-hum notch worked through.

SKU 7.2 · Sampling and aliasing

  1. Sampling theorem, Nyquist frequency and aliasing

    What sampling does to a spectrum (copies at multiples of ), the sampling theorem and the Nyquist frequency, how to compute the alias of any sampled sine wave, how time-domain and frequency-domain pictures of the same event compare, and how an anti-aliasing filter is specified.

  2. Quantisation error and the errors of sampling

    How an ADC rounds each sample to one of levels, the step size, the maximum and rms quantisation error, the SQNR rule of about per bit, what happens to signals smaller than full scale, the error caused by sampling-clock jitter, and how oversampling trades rate for resolution.

  3. Spectra of periodic and aperiodic signals

    How a periodic signal has a line spectrum given by its Fourier series and an aperiodic one a continuous spectrum given by its Fourier transform, how the two are related (lines are samples of the envelope), what sampling does to either, power by Parseval's relation, and how to read time-domain features from a spectrum and back.

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