Spectral shifting based on direct manipulation of FFT spectra. The audio output is derived from a transformed version of the input audio spectrum. The transformation involves shifting all FFT components by a selectable ratio. The characteristics of the spectral transformation are adjustable via the Parameter Window, as summarised in the following table. Stereo signals have separate adjustments for left and right channels. Parameter Purpose "Buffer length" slider Adjusts the length of the input data buffer, which also defines the "Latency" (overall delay) of the process. The FFT buffer size is computed from the "Buffer length" rounded up to the nearest power of 2 (for efficient FFT computation). If "double zero-padding" is selected, the FFT buffer size is doubled (after the rounding) to improve the smoothness of the spectrum between successive FFT bins (but without increasing the underlying frequency resolution). The input data buffer is windowed (using a selected profile), then extended to the length of the FFT buffer by padding with zeros (on either side). Successive input data buffers are overlapped by a factor of 2, and the ouputs of the overlapped inverse transformed buffers are summed, in order to avoid discontinuities at the window boundaries. "Output gain" slider Adjusts the overall gain of the output signal, after the spectral manipulations have been applied. "Frequency shift" slider Adjusts the extent of the frequency shift. Each frequency (FFT component) is shifted by the factor determined by the slider value. "Window type" selection Selects the profile of the windowing function applied to the input data.
Each successive input buffer is transformed to the frequency domain using the windowed-FFT with double overlapping. The frequency shift is implemented by moving each FFT value in proportion to the frequency of its bin multiplied by the selected shift ratio. The modified spectrum is then re-converted to the time domain (using the inverse FFT), and the overlapped output buffers are summed to yield the output signal. For an introduction to the Discrete Fourier Transform and the FFT, see, for example, [St] sections 4.1 and 4.2. For further introductory information (with emphasis on audio applications), and for discussions on spectral measurements, zero-padding, windowing, the overlap-add re-synthesis method, and the Short Time Fourier Transform (STFT) for audio applications, see [Roa] p. 1084-1112 and [Moore] p. 61-111.
