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Index: Spectral Audio Signal Processing
Spectral Audio Signal Processing
Filter Bank View of the STFT
Filter Bank View of the STFT
Overlap-Add View of the STFT
A set of filters that decompose a signal into a set of components — Click for http://en.wikipedia.org/wiki/Filter_bank
A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html
The Short Time Fourier Transform (STFT) computes the spectrum (DFT) of successive time frames of a signal. — Click for https://ccrma.stanford.edu/~jos/sasp/Short_Time_Fourier_Transform.html
The Short Time Fourier Transform (STFT) computes the spectrum (DFT) of successive time frames of a signal. — Click for https://ccrma.stanford.edu/~jos/sasp/Short_Time_Fourier_Transform.html
The Discrete Fourier Transform (DFT) computes a discrete-frequency spectrum from a discrete-time signal of finite length. — Click for https://ccrma.stanford.edu/~jos/mdft/
A signal is typically a real-valued function of time. A discrete-time signal is typically a real-valued function of discrete time, and is therefore a time-ordered sequence of real numbers. — Click for http://ccrma.stanford.edu/~jos/filters/Definition_Signal.html
In the overlap-add formulation of Chapter 8, we used a
hopping window to extract time-limited signals to which we
applied the DFT. Assuming for the moment that the hop size
(the ``sliding DFT''), we have
(10.1)
This is the usual definition of the Short-Time Fourier Transform
(STFT) (§7.1). In this chapter, we will look at the STFT from
two different points of view: the OverLap-Add (OLA) and
Filter-Bank Summation (FBS) points of view. We will show that
one is the Fourier dual of the other [9]. Next
we will explore some implications of the filter-bank point of view and
obtain some useful insights. Finally, some applications are
considered.
(the ``sliding DFT''), we have
![$\displaystyle \zbox {X_m(\omega_k) = \sum_{n=-\infty}^\infty [w(n-m) x(n)] e^{-j\omega_k n}.} \protect$](img1527.png)