Question

nin transforms and bases explain the following terms in dsp

what is vector transform and what is fft

how dft and convolution of two signals related and what property allow to decrease the burden of computation

what is convolution and what is fast convolution

difference beteen dct and dft

Answer 1

Vector tranform:

It's one kind of mapping in dsp. It's one kind of mapping where we associate vectors from on space to vectors of other space.

Fft:

Fft is an algorithm that is useful to calculate decrete Fourier tranform. Sometimes it'll also useful to calculate the inverse discrete Fourier tranform.

Convolution:

It's a mathematical operation that we do on any two signals which in turn produces the third signal. This output signal has the properties of both of those input signals.

Fast convolution:

It's a way to calculate convolution of two finite signals in a mathematical way. It's more often can be calculated by matrix multiplication.

Differences between DCT and DFT:

1)DFT uses exponential functions while DCT uses cosine functions.

2) DFT is mainly used is spectral analysis applications while DCT is mainly used in image compression applications.

Convolution and DFT:

Convolution thoerm is used in frequency domain to calculate convolution of two signals. Convolution in time domain leads to multiplication in frequency domain. This is the main idea about convolution thoerm.