frequencyshifting

Frequency shifting is a signal processing operation that relocates the spectrum of a signal by a fixed offset, Δf. In other words, every spectral component at frequency f is translated to f + Δf. In practice, this is commonly achieved by mixing the signal with a complex exponential of frequency Δf, typically after forming an analytic (complex-valued) representation so that the shift does not create unwanted mirror components. For real-valued signals, straightforward multiplication by a cosine can produce image frequencies, so analytic methods or quadrature mixing are used to realize a true, single-sided shift.

In hardware, frequency translation is often realized by mixing the input with a local oscillator in a nonlinear device. The mixer produces sum and difference frequencies, and a subsequent filter selects the desired shifted output. In digital signal processing, frequency shifting can be implemented via complex multiplication with e^{j2πΔf t} on the analytic signal, or with phase-vocoder, Hilbert-transform-based approaches, or other time- and frequency-domain methods. These methods aim to shift the spectrum while controlling artifacts and preserving or altering other signal attributes such as formants in audio.

Applications span radio communications, where frequency translation moves signals to convenient bands, to audio processing, where a frequency shifter creates effects or preserves pitch without altering duration. Limitations include potential spectral artifacts, image interference, and distortion of transient and formant structures; careful filtering and processing are often required, especially for broadband or high-dynamic-range signals.

See also: heterodyning, upconversion, downconversion, phase vocoder, analytic signal, pitch shifting.