Skills Mapping
Dr M. Fullekrug - 20/01/2025
Skills ? :
Spectogram_Generation_and_Analysis.md
Schedule:
Thursday, Week 11 .

Signal Processing

Spectral Analysis.

Introduction

The objective of this laboratory is to gain an understanding of spectral analysis in digital signal processing. The laboratory requires the use of matlab on the command line, similar to the examples shown during the lectures. Immediate formative feedback on the answers is provided when accessing the laboratory at https://moodle.bath.ac.uk/mod/quiz/view.php?id=1395946 :

The completion of the spectral analysis laboratory helps to claim the corresponding skill. Download the file ml1skill.p from https://people.bath.ac.uk/eesmf/LECTURES/SPCW and run the .p file in matlab. The matlab file offers feedback on the completion of the skill. Upon successful completion, upload the resulting .pdf to the portfolio on Mahara.

Part A - Spectral Analysis

Download the file mlab1a.mat from https://people.bath.ac.uk/eesmf/LECTURES/SPCW

  • Single frequency – use the signal y1
  • (01 - 1) Calculate the sampling time interval of the recordings in s.
  • (02 - 1) Determine the number of samples in the recordings.
  • (03 - 1) Calculate the total duration of the recordings in s.
  • (04 - 1) Calculate the fundamental harmonic frequency of the recordings f1 in Hz.
  • (05 - 1) Determine the frequency of the signal in the recordings in Hz.
  • (06 - 1) Calculate the spectral amplitude of the signal in the recordings.
  • Two frequencies – use the signal y2
    • (07 - 1) Calculate the frequency resolution of the spectrum in Hz.
    • (08 - 1) Determine the larger frequency of the signal in the recordings in Hz.
    • (09 - 1) Calculate the phase of the larger frequency component in rad.
    • (10 - 1) Calculate the harmonic number for the smaller frequency component.
    • (11 - 1) Calculate the harmonic number for the larger frequency component.
    • (12 - 1) Apply the Hanning window to the signal. How many spectral peaks are present?
  • Leakage – use the signal y3
    • (13 - 1) Calculate the spectrum of the signal y3. Plot the spectrum on the log scale. How many spectral peaks are present?
    • (14 - 1) Apply the Hanning window to the signal y3. Plot the spectrum on the log scale. How many spectral peaks are present?
    • (15 - 1) Estimate the most likely frequency of the signal located between 104-120 Hz in the spectrum in Hz.

Part B - Unit Phasor

Download the file mlab1b.mat from https://people.bath.ac.uk/eesmf/LECTURES/SPCW

  • unit phasor – use the unit phasor z
    • (16 - 2) Determine the frequency of the unit phasor in Hz.
    • (17 - 2) Determine the mirror frequency of the conjugate unit phasor in Hz.
    • (18 - 2) Determine the negative frequency of the conjugate unit phasor in Hz.
  • signal and unit phasor – use the complex signal y and the unit phasor z
    • (19 - 2) Determine the frequency of the complex signal y
    • (20 - 2) Calculate the product of the complex signal and the conjugate unit phasor. Determine the frequency of this product in Hz.
    • (21 - 2) Calculate the product of the complex signal and the conjugate unit phasor. Calculate the phase of this product at the time 0.25 s and give the result in rad.

Part C - Real World signals

Download the file mlab1c.mat from https://people.bath.ac.uk/eesmf/LECTURES/SPCW

  • Wineglass resonance – use the signal y1
    • (22 - 3) Determine the frequency of the dominant peak in the spectrum in Hz.
    • (23 - 3) Calculate the amplitude of the dominant peak in the spectrum.
    • (24 - 3) Calculate the phase of the dominant peak in the spectrum in rad.
  • Piano tone – use the signal y2
    • (25 - 3) Determine the frequency of the dominant peak in the spectrum in Hz.
    • (26 - 3) Plot the spectrum on the log scale. How many significantly outstanding spectral peaks are present in the spectrum from 0-2500 Hz?
    • (27 - 3) Apply the Hanning window to the signal y2. Plot the spectrum on the log scale. Determine the frequency in Hz of the second largest peak which is to the right of the dominant peak at a slightly larger frequency between 440-446 Hz.
  • Spectrogram – use the signal y3
    • (28 - 3) The spectrogram of y3 contains an important message. State that message

Part D - Phase change

Download the file mlab1d.mat from https://people.bath.ac.uk/eesmf/LECTURES/SPCW

  • Phase change of signal – use the signal y
    • (29 - 4) Determine the frequency of the signal in kHz by calculating a spectrogram with 1 kHz resolution, using a rectangular window with no overlap.
    • (30 - 4) Determine the temporal resolution of the spectrogram in ms.
    • (31 - 4) Determine the frequency of the signal’s phase change in Hz by calculating a spectrum using the complex spectral coefficients of the signal in the spectrogram.
    • (32 - 4) Calculate the start phase of the signal’s phase change.

Citations