A. Table of contents by sections: 1. Abstract (you’re reading this now) 2. Summary of the DFT (How do I do the homework?) 3. Review of continuous-time Fourier series 4. Bandlimited signals and finite Fourier series 5. Sampling theorem for periodic signals 6. Review of quirks of discrete-time frequency 7. Orthogonality and its significance 8. Discrete Fourier Transform (DFT) 9. Use of DFT to com...

In this contribution we generalize the classical Fourier Mellin transform [3], which transforms functions f representing, e.g., a gray level image defined over a compact set of R. The quaternionic Fourier Mellin transform (QFMT) applies to functions f : R → H, for which |f | is summable over R+ × S under the measure dθ dr r . R ∗ + is the multiplicative group of positive and non-zero real numbe...

1 Motivation We want to numerically approximate coefficients in a Fourier series. The first step is to see how the trapezoidal rule applies when numerically computing the integral (2π) −1 2π 0 F (t)dt, where F (t) is a continuous, 2π-periodic function. Applying the trapezoidal rule with the stepsize taken to be h = 2π/n for some integer n ≥ 1 results in (2π) −1 2π 0 F (t)dt ≈ 1 n n−1 j=0 Y j , ...

T he difficulties that always plague an experimental spectroscopist are those associated with resolving power, light-gathering ability, and wavelength and photometric accuracy. He sees a spectrum, such as that of atmospheric water vapor shown in Fig. 1, and deduces from it information about the atoms or molecules which gave rise to it. Such spectrograms can be taken at wavelengths from the far ...

The discrete Fourier transform (DFT) maps a nite number of discrete time-domain samples to the same number of discrete Fourier-domain samples. Being practical to compute, it is the primary transform applied to real-world sampled data in digital signal processing. The DFT has special relationships with the discrete-time Fourier transform and the continuous-time Fourier transform that let it be u...

In signal processing applications, a key role is played by the Fourier transforms. The mathematical structure underlying Fourier analysis is the linear structure. In the present paper we propose and study a tool designed for nonlinear signal and image processing, that is novel Fourier-like transforms, based on a pair of pseudo-operations consisting of a uninorm and an absorbing norm. We analyse...

This note provides a brief review of the Fourier transform for the analysis of discretetime signals and systems and a description of practical assignments, which will be performed on a Texas Instrument DSP board. Some tasks are to be performed with the help of MATLAB. It is assumed that the student has enough theoretical background to perform the practical part of the work. The review of some a...

This paper describes a novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars. The technique is based on the use of serial storage for data and intermediate results and multiple arithmetic units each of which carries out a sparse Fourier transform. Deta...

• Forward and Inverse 32-, 64-, 128-, 256-, 512-, 1,024-, and 2,048-Point Complex FFT • Decimation–In-Time (DIT) Radix-2 Implementation Optimized for Actel FPGAs • Selection of Unconditional or Conditional Block Floating-Point Scaling • Embedded RAM-Block-Based Twiddle Factor Generator • 8to 16-Bit Configurable Input/Output Data and Twiddle Coefficients Precision • Naturally Ordered Input and O...