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Jupyter Notebook: Explore the Spectrogram

February 16, 2023 by allsignal

Spectrogram of a linear chirp and several sinusoids.

You will use the spectrogram to identify features in signals whose spectra vary with time, including a brief guitar solo and synthetic signal composed of a chirp and sinusoids. You will learn about the tradeoff between temporal resolution and resolution of features in the frequency domain by changing the DFT length used by the spectrogram.

Prerequisites

Using Jupyter Notebooks

Jupyter Notebook: Explore the Windowed DFT

The Short-Time Fourier Transform and the Spectrogram

Files

Explore the Spectrogram


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Course Lessons

  • Discrete Fourier Transform: Sampling the Discrete-Time Fourier Transform

  • Important Discrete Fourier Transform Properties

  • Fast Fourier Transform (FFT) Algorithm

  • Introduction to Circular Convolution and Filtering with the Discrete Fourier Transform

  • Circular Convolution Property of the Discrete Fourier Transform

  • Filtering with the Discrete Fourier Transform

  • The Discrete Fourier Transform Approximation to the Fourier Transform

  • The Effect of Windowing on the Discrete Fourier Transform Approximation to the Fourier Transform

  • Windows and the Discrete-Time Fourier Transform: Trading Resolution for Dynamic Range

  • An Example of Approximating the Fourier Transform with the Discrete Fourier Transform

  • Jupyter Notebook: Explore the Windowed DFT

  • The Short-Time Fourier Transform and the Spectrogram

  • Jupyter Notebook: Explore the Spectrogram

  • A Matrix Interpretation of the Discrete Fourier Transform

  • A Matrix Interpretation of the Fast Fourier Transform Algorithm

Courses

  • Foundations

  • Time Domain LTI Systems

  • 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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