NivaarExam Prep

22-Elec-A3 Signals and Communications

Worked solutions to 14 past sittings (2013–2019), 84 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.

Questions by sitting

December 2019

  1. Question 1: Full-Wave Rectifier — Fourier Series, Band-Pass Filtering and Power
  2. Question 2: Two-Tone Message — Exact Spectra, DSB, SSB and Frequency Translation
  3. Question 3: PCM System Design — Quantisation Levels, Noise Power and Bit Rate
  4. Question 4: FIR System from its Impulse Response — Structure, Transfer Function, Response and Stability
  5. Question 5: FM Modulator Driven by a Rectangular Message — Deviation, Signal Form, Carson Bandwidth and Demodulation

December 2018

  1. Question 1: Threshold Device Driven by a Cosine — Fourier Series, Filtering and Power
  2. Question 2: Uniform PCM — Signal-to-Quantisation-Noise Ratio and Bit Rate
  3. Question 3: Spectra of a Composite Message under DSB and SSB Modulation
  4. Question 4: Discrete-Time System — Transfer Function, Impulse and Frequency Response
  5. Question 5: Square-Law Frequency Downconverter — IF Selection and Filter Bandwidth

May 2018

  1. Question 1: Fourier Series of a Rectangular Pulse Train — Harmonic Amplitude, Power and Duty-Cycle Optimisation
  2. Question 2: Uniform PCM of a Speech Signal — Sampling, Step Size, Levels, SNR and Bit Rate
  3. Question 3: Amplitude Modulation — Time Waveform, Spectrum, Envelope and Two Demodulators
  4. Question 4: Discrete-Time LTI System — Delayed-Step Response and Frequency Response
  5. Question 5: Spectral Mirroring and Frequency Conversion with a Limited Oscillator

December 2017

  1. Question 1: Frequency Doubler — Full-Wave Rectifier and Ideal Band-Pass Filter
  2. Question 2: Discrete-Time System — Transfer Function, Impulse Response and Pulse Response
  3. Question 3: Amplitude Modulation with a Triangular Message
  4. Question 4: PCM System with Uniform Quantisation
  5. Question 5: Superheterodyne Receiver — Image Frequency and Front-End Design

May 2017

  1. Question 1: First-Order RC Low-Pass Filter Driven by a Square Wave
  2. Question 2: Discrete-Time LTI System — Convolution, Structure and Stability
  3. Question 3: DSB and AM Modulation of a Two-Tone Message
  4. Question 4: Non-Uniform PCM Quantizer Design for a Voice Signal
  5. Question 5: Angle-Modulated Signal — Message Recovery, Deviation and Bandwidth

December 2016

  1. Question 1: Periodic Square Wave through Ideal Low-Pass and High-Pass Filters
  2. Question 2: Discrete-Time System — Realisation, Impulse Response and Stability
  3. Question 3: DSB and AM Modulation of a Staircase Message
  4. Question 4: PCM Transmission of a Video Signal
  5. Question 5: Spectra of DSB and SSB Modulation, Coherent Detection and Frequency Translation
  6. Question 6: VCO-Based FM Modulator, Demodulator and Carson Bandwidth

May 2016

  1. Question 1: Fourier Transform, Energy and Ideal Low-Pass Filtering
  2. Question 2: Quadrature Modulation, Coherent Demodulation and Envelope Detection
  3. Question 3: PCM — Bit Rate, Quantizer Resolution and Analog Bandwidth
  4. Question 4: AM — Time-Domain Expression, Spectrum and Bandwidth
  5. Question 5: Discrete-Time System — Realisation, Transfer Function and Step Response
  6. Question 6: FM Modulator Output, Carson Bandwidth and Demodulation

December 2015

  1. Question 1: Discrete-Time System — Transfer Function, Stability and Impulse Response
  2. Question 2: Fourier Series, Power Spectral Density and Band-Pass Filtering
  3. Question 3: Amplitude Modulation — Waveform, Efficiency, Spectrum and Detection
  4. Question 4: PCM Transmission of an Audio Signal
  5. Question 5: Frequency Modulation with a Two-Tone Phase Deviation
  6. Question 6: Spectral Inversion and Frequency Conversion

May 2015

  1. Question 1: Periodic Ramp Train — Fourier Series, Power Spectral Density and Ideal Filtering
  2. Question 2: Second-Order Discrete-Time System — Transfer Function, Impulse Response and Canonical Realisation
  3. Question 3: Conventional AM — Power Budget, Spectrum, Envelope and Detection
  4. Question 4: PCM of a Speech Signal — Sampling, Quantization and Bit Rate
  5. Question 5: Square-Law Frequency Downconverter — Choice of IF and Filter Bandwidth
  6. Question 6: FM Signal Processing — Multiplication, Frequency Translation, Demodulation and Squaring
  7. Question 7: Speech Scrambler — Spectral Inversion and its Inverse

December 2014

  1. Question 1: Fourier transform, spectra, energy and filtering of a delayed exponential
  2. Question 2: Half-wave rectifier, a.c. coupling and integration of a cosine
  3. Question 3: PCM design: sampling rate, word length, bit rate and multiplexed bandwidth
  4. Question 4: Modulator outputs and demodulators for a square-wave message
  5. Question 5: Superheterodyne receiver: local-oscillator choice, image frequency and band planning
  6. Question 6: Discrete-time system: difference equation, transfer function, impulse response and stability
  7. Question 7: AM with a triangular message: time expression, spectrum, envelope and detectors

May 2014

  1. Question 1: Sampling and Reconstruction of a Squared-Sinc Signal
  2. Question 2: Sampling a Two-Tone Message, With and Without Aliasing
  3. Question 3: Scaling, Shifting and Modulation of a Sinc Pulse
  4. Question 4: Reading an FM Spectrum with Bessel Coefficients
  5. Question 5: PCM Design for a Television Signal
  6. Question 6: AM Signal Parameters, Power Budget and Efficiency
  7. Question 7: Testing a Cascade for Linearity and Distortionlessness
  8. Question 8: Regions of Convergence and Impulse Responses of a Discrete System
  9. Question 9: M-ary PCM Bandwidth for an Audio Channel
  10. Question 10: Matched Filtering and Decoding of Split-Phase Manchester Data

December 2013

  1. Question 1: Fourier Series Spectra of a Multi-Tone Signal
  2. Question 2: Recovering the Message from an Angle-Modulated Signal
  3. Question 3: Impulse Sampling of a Squared-Sinc Signal
  4. Question 4: Fourier-Transform Properties Without Computing the Transform
  5. Question 5: Inverse z-Transform by Partial Fractions, Two Ways
  6. Question 6: Transmitter Power Budget for AM and DSB

May 2013

  1. Question 1: Impulse Response and Direct Form II Realisation
  2. Question 2: Graphical Convolution of a Pulse with a Triangle
  3. Question 3: Exponential Fourier Series of a Triangular Wave
  4. Question 4: Fourier Transforms and Spectra of Two-Sided Exponentials
  5. Question 5: Envelope Detection of DSB-SC Signals
  6. Question 6: Baseband, DSB-SC, USB and LSB Spectra

Undated paper

  1. Question 1: Fourier Series of a Pulse Train Through a Filter Cascade
  2. Question 2: Non-Uniform (Two-Range) PCM Quantizer Design
  3. Question 3: DSB, Full AM and SSB of a Two-Component Message
  4. Question 4: Recovering the Message from an Angle-Modulated Signal
  5. Question 5: Transfer Function and Realisation of a Two-Tap FIR Filter