22-Elec-B1 Digital Signal Processing
Worked solutions to 9 past sittings (2013–2019), 53 questions. Pick a sitting, or start from a topic below.
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Circular convolution (3 sittings): December 2019 Q2 · May 2014 Q4 · May 2013 Q1
- Impulse Response (3 sittings): December 2019 Q3 · May 2017 Q3 · May 2014 Q6
- Stability (3 sittings): December 2019 Q4 · May 2014 Q1 · Undated paper Q4
- Circular Shift (2 sittings): December 2019 Q2 · December 2013 Q5
- Linear convolution (2 sittings): May 2018 Q2 · May 2015 Q5
- Sinusoidal Steady State (2 sittings): May 2014 Q6 · December 2013 Q3
- Step response (2 sittings): December 2013 Q3 · May 2013 Q3
- System function (2 sittings): May 2018 Q5 · May 2017 Q3
Questions by sitting
December 2019
- Question 1: Sampling Followed by Ideal Reconstruction
- Question 2: Six-Point DFT, Circular Shift and Circular Convolution
- Question 3: Impulse Response, Output and Stability of a First-Order System
- Question 4: Stability and Structures for a Parallel System
- Question 5: Kaiser Window Design of a Three-Band FIR Filter
- Question 6: IIR Design Choices and Linear-Phase FIR Types
May 2018
- Question 1: Sampling rate, effective analogue cut-off and the reconstructed spectrum
- Question 2: Eight-point circular convolution versus linear convolution
- Question 3: Direct form II and transposed flow graphs
- Question 4: Frequency-domain sampling and the resulting time aliasing
- Question 5: System function, all admissible ROCs and the value of $h[0]$
- Question 6: Which linear-phase FIR types can realise each desired response
May 2017
- Question 1: Sampled-data differentiator and the band-limit condition
- Question 2: Recovering the DFT length from a circular shift
- Question 3: System function, ROC, impulse response and difference equation
- Question 4: Direct form I and transposed direct form II flow graphs
- Question 5: Identifying filter families from pole-zero plots
- Question 6: Reading a Kaiser-window highpass design backwards
May 2016
- Question 1: Reconstructing a real sequence from six frequency-domain clues
- Question 2: Continuous-time filtering by a discrete-time lowpass filter at three sampling-rate pairs
- Question 3: ROC, realness and z-domain scaling of a causal stable system
- Question 4: Filling in a four-section cascade flow graph
- Question 5: Computing an inverse DFT with a forward FFT subroutine
- Question 6: Kaiser-window highpass design — recovering the specifications and repairing the error at $\omega=\pi$
May 2015
- Question 1: Reconstructing a real causal sequence from six transform clues
- Question 2: Sampling a band-limited periodic signal
- Question 3: Pole-zero transformations of a causal stable system
- Question 4: Parallel and cascade realisations of an IIR system
- Question 5: Circular versus linear convolution, and the FFT route
- Question 6: IIR design by transformation and the four linear-phase FIR types
May 2014
- Question 1: Pole-Zero Diagrams, ROC, Stability and Causality
- Question 2: FIR and IIR Notch Filter Design from a DFT Spectrum
- Question 3: Applying the DFT Twice: Recovering the Original Sequence
- Question 4: One Output, Four Methods: Iteration, Convolution, Circular Convolution and the DFT
- Question 5: System Reconstruction from Poles, Zeros and d.c. Gain
- Question 6: Impulse Response, Frequency Response and Sinusoidal Steady State
- Question 7: Computing the IDFT with a Forward-DFT Block
December 2013
- Question 1: Impulse and Frequency Response of a Three-Tap FIR System
- Question 2: Convolution of a Rectangular Window with an Impulse Train
- Question 3: Causal System Function — Step Response, Inverse Filtering and Sinusoidal Steady State
- Question 4: Continuous-Time Filtering by a Discrete-Time System — Three Sampling-Rate Cases
- Question 5: Six-Point DFT Properties — Circular Shift, Symmetry and Frequency Decimation
May 2013
- Question 1: Linear and circular convolution, the two-point DFT butterfly, and block filtering
- Question 2: Transfer function from a pole/zero plot and multiplier-free realisations
- Question 3: Region of convergence, step response and the inverse system
- Question 4: Four-point DFTs and circular convolution
- Question 5: Interpolation, band-pass selection and the equivalent continuous-time system
Undated paper
- Question 1: Sampling rate for an ideal C/D – filter – D/C chain
- Question 2: Periodic convolution from a product of discrete Fourier series
- Question 3: Why a longer zero-padded DFT runs faster
- Question 4: Partial fractions, stability and causality from the ROC
- Question 5: Five signal flow graphs for one third-order system
- Question 6: Kaiser-window design of a linear-phase bandpass filter