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When to use DCT and DFT in signal processing?
When you are transforming a signal in to a frequency domain using both DFT and DCT, say for a function sin (x), how the spectrum will be? will both frequency values (of DCT and DFT) same? Can anyone explain the values of the frequencies for the function sin (x) (obviously the frequency should be 1/2π)
How are phase spectra used to calculate delay spread?
If you compare the amplitude spectra of a reference signal with its corrupted version, you get the information about the way noise effected this signal. Consequently, if you compare the phase spectra of these two signals, you get the delay spread information or dispersion, the information about phase distortion.
Is the phase spectrum an essential piece of info?
This means that the phase spectrum is an essential piece of info (along with the magnitude). Alternatively, one can represent the signal by its I and Q (in phase and quadrature components). Complex representations of signals always have two components, magnitude and phase or real and imaginary parts.
How is the amplitude spectrum related to the phase spectrum?
Graphical presentation of these two quantities as function of frequency gives amplitude spectrum (characteristics) and phase spectrum (characteristics). Amplitude and phase, for a given frequency and given signal, can be calculated from Fourier transform. Both of them usually are a function of frequency, i.e. A (f) and Phi (f).
Which is the second transform of the DFT?
The particular algorithm is defined as Fourier transform -> square of magnitude -> mel filter bank -> real logarithm -> discrete cosine transform. Here DCT can be selected as the second transform, because for real-valued input, the real part of the DFT is a kind of DCT.
Are there any boundary conditions between DST and DFT?
Yes. More specifically, the DFT has periodic boundary conditions, the DCT has derivative zero (Neumann) boundary conditions, and DST has the value zero (Dirichlet) boundary conditions. For images and audio, the boundary effects are less noticeable in the DCT case.
Why is DCT chosen as the second transform?
Here DCT can be selected as the second transform, because for real-valued input, the real part of the DFT is a kind of DCT. The reason why DCT is preferred is that the output is approximately decorrelated. Decorrelated features can be modelled efficiently as a Gaussian distribution with a diagonal covariance matrix.