DATA 3464: Fundamentals of Data Processing

Signals and Audio

Charlotte Curtis
March 17, 2026

Topic overview

  • Introduction to signals
  • Audio as a 1D signal
  • File formats
  • A brief intro to signal processing

Resources used:

  • Various textbooks from my undergrad
  • DSPguide.com seems like a pretty good resource

What is a signal?

"A [continuous/discrete] signal is a function of independent variables that range over [a continuum/discrete] values" - Jerry L. Prince, Medical Imaging Signals and Systems

  • Common notation: for continuous, for discrete
  • Signals are discretized by sampling at some fixed interval
  • The sampling rate is informed by the frequency content of the data:

    (but in practice is much higher)

Frequency content of a signal

  • A discrete time domain signal can be represented as:

  • Or, using Euler's formula :

    where the complex coefficients and

Fourier Transform

  • To figure out what the coefficients are, we can use the Discrete Fourier Transform (DFT):

    where each element of is the coefficient for frequency
  • This can also be inverted to get back the original signal:

This is skipping over several entire math courses

Where we left off on March 17

Symmetry in the frequency domain

  • Since a real-valued signal in time is composed of both sine and cosine components, its DFT has conjugate symmetry

    where denotes the complex conjugate
  • This means the negative-frequency half of the spectrum is redundant
  • In practice, for real-valued data, we often only inspect:
    • magnitude: to see "how much" of each frequency is present
    • phase: to see alignment/shift information

Frequency vs Time Domains

center

  • short time = high frequency, small frequency = long time

Example signal: Audio

  • Once you think of a signal as being a weighted sum of frequency components, you can do some fun things with it
  • We can extract information, downsample, remove noise, etc
  • Example: a typical .wav file
    • Uncompressed
    • 16 bits per sample (bit depth)
    • 48 kHz sampling rate
    • mono (1 channel) or stereo (2 channels)

What about .mp3? .ogg? I would use ffmpeg to convert to .wav

Preparing data

  • Assuming we're starting with a collection of audio files, we can either:
    • Extract features and save as tabular data
    • Use the raw audio signal as input
  • We can preprocess and store the data, or preprocess on the fly

What considerations might go into this decision?
What should always be stored regardless of the approach?

Preparing audio data

  • Data for learning tasks is easiest to work with if it is consistent
  • For audio signals, this could include:
    • Decompressing and converting to .wav
    • Downsampling
    • Aligning and cropping primary signal
    • Converting to mono/stereo
    • Extracting features
  • librosa can help with this (and can apparently handle mp3 too!)

Coming up next

  • 2D signals (aka images)
  • Strategies and software for labelling data

By next week you should have some idea of what kind of dataset you want to curate and label for Assignment 3