Does frequency have to be an integer?
There does not have to be an integer number of cycles in one second. With non periodic signals, there is no one fundamental frequency associated with them, no repeating pattern – they can maybe be thought of as a periodic function with an infinite period.
Why are harmonics integers?
harmonics are always created for the odd integers i.e. 3rd,5th,7th etc. It is because if we do a fourier transform on a current/voltage wave, we will find out that the highest amount of distortions occur in this principal values harmonic distortions always occur on this values.
Does frequency have to be a whole number?
No. By definition: Harmonics, are frequencies which are integral multiples of the fundamental (including the fundamental which is 1 times itself). It need to be appreciated that non-whole numbers are not integers. In Fourier analysis of a signal, the fundamental and its overtones together are called partials.
Is the DFT a continuous representation of the original sequence?
The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle.
How is a discrete Fourier transform implemented in a computer?
Discrete Fourier transform. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware. These implementations usually employ efficient fast Fourier transform (FFT) algorithms; so much so that the terms “FFT” and “DFT” are often used interchangeably.
What is the convolution theorem for the DTFT?
The convolution theorem for the discrete-time Fourier transform (DTFT) indicates that a convolution of two sequences can be obtained as the inverse transform of the product of the individual transforms.