series_ifft

This page explains how to use the series_ifft function in APL.

The series_ifft function applies the Inverse Fast Fourier Transform (IFFT) on a series, taking a series of complex numbers in the frequency domain and transforming it back to the time/spatial domain using the Fast Fourier Transform. This function is the complementary function of series_fft. Commonly the original series is transformed to the frequency domain for spectral processing and then back to the time/spatial domain.

You can use series_ifft when you want to reconstruct time-domain signals from frequency-domain data, implement frequency-domain filtering, or perform signal synthesis. This is particularly useful after applying frequency-domain operations like filtering or when you need to convert processed frequency data back to the original time domain. Typical applications include signal reconstruction, frequency-domain filtering, noise reduction, and advanced signal processing workflows.

Usage

Syntax

APL

series_ifft(fft_real [, fft_imaginary])

Parameters

Parameter	Type	Description
`fft_real`	dynamic	A dynamic array of real numeric values representing the real component of the series to transform.
`fft_imaginary`	dynamic	Optional: A dynamic array of real numeric values representing the imaginary component of the series. Only specify this if the input series contains complex numbers.

Returns

The function returns the complex inverse FFT in two series. The first series for the real component and the second one for the imaginary component.

Example

The example below shows how series_ifft reverses the effect of series_fft by reconstructing the original time-domain signal from frequency-domain data.

Query

APLRun in Playground

['sample-http-logs']
| summarize durations = make_list(req_duration_ms) by bin(_time, 1h)
| extend reconstructed_durations = series_ifft(series_fft(durations)[0])

Output

durations	reconstructed_durations
0.5848084109504474	0.5848084110671455
0.5506109370041884	0.5506109371007348

series_fft: Performs Fast Fourier Transform to convert time domain to frequency domain. Use before applying frequency-domain operations.
series_fir: Applies a finite impulse response filter to a series. Use for time-domain filtering instead of frequency-domain processing.
series_cos: Returns the cosine of each element in an array. Use for generating periodic components in signal synthesis.
series_sin: Returns the sine of each element in an array. Use for generating periodic components with phase shifts.
series_exp: Calculates the exponential of each element in an array. Use for exponential signal components instead of frequency reconstruction.