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Sinusoidal Signals Examples

February 8, 2019 by 3200 Creative

This lesson illustrates sinusoidal signals with two examples drawn from music. In the first example you will see how changing the frequency of sinusoids can generate the notes in a musical scale. The second example previews the important topic of Fourier representations. You will see and hear that as few as eight sinusoids accurately represent the sound produced by a saxophone.

Prerequisites

  • Sinusoidal Signals

Key Concepts and Screenshots

Concepts and Slides: Sinusoidal Signals Examples

Supplementary Material

  • m-file Sinusoidal Signals Examples
  • .mat file containing Saxophone note A
  • Music Scale

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/music_scale.wav
  • Saxophone Note A

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxA.wav
  • Representation of Saxophone Note A with One Sinusoid

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxApprox_1comps.wav
  • Representation of Saxophone Note A with Two Sinusoids

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxApprox_2comps.wav
  • Representation of Saxophone Note A with Three Sinusoids

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxApprox_3comps.wav
  • Representation of Saxophone Note A with Six Sinusoids

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxApprox_6comps.wav
  • Representation of Saxophone Note A with Eight Sinusoids

  • https://allsignalprocessing.com/ASP-Downloads/Foundations/SinusoidalSignalsExamples/SaxApprox_8comps.wav
    QuizzesStatus
    1

    Sinusoidal Signals Examples


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    • Signals Everywhere

    • Ever-Present Noise

    • Models, Math, and Real-World Signals

    • Four Signal-Processing Themes

    • Building Signals with Blocks: Basis Expansions

    • Jupyter Notebook: Explore FIR Filtering

    • Jupyter Notebook: Explore Image Filtering

    • Signals: The Basics

    • Sinusoidal Signals

    • Sinusoidal Signals Examples

    • Complex Sinusoids

    • Exponential, Step, and Impulse Signals

    • Introduction to Linear, Time-Invariant Systems

    • Introduction to Difference Equation System Descriptions

    • Impulse Response Descriptions for LTI Systems

    • Frequency Response Descriptions for LTI Systems

    • Introduction to the System Function and System Poles and Zeros

    • The Four Fourier Representations

    • Summary Problems for Foundations

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    • Fourier Series and Transforms

    • Sampling and Reconstruction

    • The DFT and Applications

    • The Z-Transform

    • Intro to Filter Design

    • IIR Filter Design

    • FIR Filter Design

    • Random Signal Characterization

    • Basis Representations of Signals

    • Estimation of Power Spectra and Coherence

    • Introduction to Signal Estimation and Detection Theory

    • MMSE Filtering and Least-Squares Problems

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