**Overlap**: 25% and 50% overlaps are common. A regular process is:

- segment into 50% overlapped frames
- window each frame (ex Hamming window, blackman window)
- add overlaps to reconstruct

Use ‘segment/window/overlap’ to smooth out the transitions between different processing domains since there is a discontinuity between neighboring frames, and that makes it as a clicking sound.

A single FFT can trade off between higher frequency resolution (more samples) or higher time resolution (fewer samples), but cannot do both simultaneously.

**Windowing**:

The windowed DFT is the product of the original signal and the windowing function: x[n] is a signal of infinite extend, n is the sample index, g[n] is a finite window

In frequency domain this is a convolution with the window DFT:

Here is the impact of windowing:

**Spectrogram**:

Short-time Fourier transform (STFT) is a sliding-window narrow Fourier transform that is repeated sequentially over a long vector of samples. A spectrogram is essentially a set of STFT plotted as frequency against time with the intensity (z-axis) given as a grey scale, or color pixel.

The horizontal axis of an FFT plot is traditionally used to represent frequency, and the vertical axis would display amplitude. A spectrogram plots time along the horizontal axis, frequency on the vertical and amplitude on the z-axis (as color or grey scale).

Filters:

Filters are designed based on specifications given by:

- spectral magnitude emphasis
- delay and phase properties through the group delay and phase spectrum
- implementation and computational structures

Matlab functions for filter design

- (IIR)
*besself, butter, cheby1, cheby2, ellip, prony, stmcb* - (FIR)
*fir1, fir2, kaiserord, firls, firpm, firpmord, fircls, fircls1, cremez* - (Implementation)
*filter, filtfilt, dfilt* - (Analysis)
*freqz, FDAtool, SPtool*

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