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...

magnetotelluric (mt) method is an important passive surface geophysical method which uses the earth’s natural electromagnetic fields to investigate the electrical resistivity structure of the subsurface. the depth of investigation of mt is much higher than that of other electromagnetic (em) methods (vozoff, 1991). for a general conductivity distribution in the earth, the horizontal electric fie...

Given a signal and its Fourier transform, we derive formulas for its polyphase decomposition in the frequency domain and for the reconstruction from the polyphase representation back to the Fourier representation. We present two frequency-domain implementations of the shift-invariant periodic discrete wavelet transform (SI-DWT) and its inverse: one that is based on frequency-domain polyphase de...

in this paper, a smart method is designed in order to classify healthy and illness ducks using their emission voice. for this purpose, firstly, the birds based on their healthy condition are divided into the different categories and then their voices are saved using a microphone and data acquisition card. gained signals were transformed from time-domain signal to frequency domain using fast fou...

Although semi-blind and blind watermarking schemes based on Discrete Cosine Transform (DCT) or Discrete Wavelet Transform (DWT) are robust to a number of attacks, they fail in the presence of geometric attacks such as rotation, scaling, and translation. The Discrete Fourier Transform (DFT) of a real image is conjugate symmetric, resulting in a symmetric DFT spectrum. Because of this property, t...

Estimation of fundamental frequency component of current and / or voltage signals is essential for relaying decision in most of the numerical algorithms used for the protection of power system components. Modern numerical relays generally use discrete Fourier transform for extracting the fundamental component from the post fault signals consisting of fundamental as well as non-fundamental frequ...

In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...

A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a tran...

In engineering, digital signal processing techniques need to be carefully selected according to the characteristics of the signals of interest. The frequency-based and time-frequency techniques have been frequently mentioned in some literature (Cohen, 1995). The frequencybased techniques (FBTs) have been widely used for stationary signal analysis. For nonstationary signals, the time-frequency t...