Bounded-Magnitude Discrete Fourier Transform

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Bounded-Magnitude Discrete Fourier Transform

Sebastian J. Schlecht; Vesa Välimäki; Emanuël A.P. Habets

Analyzing the magnitude response of a finite-length sequence is a ubiquitous task in signal processing. However, the discrete Fourier transform (DFT) provides only discrete sampling points of the response characteristic. This work introduces bounds on the magnitude response, which can be efficiently computed without additional zero padding. The proposed bounds can be used for more informative visualization and inform whether additional frequency resolution or zero padding is required.

The DFT is one of the prime analysis methods for spectral content of a finite-length signal [1]. The DFT, usually computed by applying the fast Fourier transform algorithm, is used for analysis and processing in many applications. Primarily, the magnitude of the DFT is commonly used for signal analysis and visualization purposes, as it describes the strength of the individual frequency components.

Although a DFT of sufficient length carries the complete information of the sequence, direct visualization of the DFT magnitude points can be hard to interpret; see Figure 1 for an example. Many pieces of scientific computing software readily provide plotting features connecting the individual DFT data with line segments. However, such a linear interpolation can be misleading, as the actual shape of the magnitude response is described by the discrete-time Fourier transform (DTFT); see Figure 1. Numerically, the DTFT is usually approximated by a zero-padded higher-order DFT. While sufficient zero padding can lead to higher accuracy, it is often not clear how much zero padding is required.

SPS on Twitter

  • DEADLINE EXTENDED: The 2023 IEEE International Workshop on Machine Learning for Signal Processing is now accepting…
  • ONE MONTH OUT! We are celebrating the inaugural SPS Day on 2 June, honoring the date the Society was established in…
  • The new SPS Scholarship Program welcomes applications from students interested in pursuing signal processing educat…
  • CALL FOR PAPERS: The IEEE Journal of Selected Topics in Signal Processing is now seeking submissions for a Special…
  • Test your knowledge of signal processing history with our April trivia! Our 75th anniversary celebration continues:…

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar