# 2.11.18 stft(Pro)

Analysis : Signal Processing : STFT

## Brief Information

Compute short time fourier transform of signal

This feature is for OriginPro only.

## Command Line Usage

 1. stft ix:=col(2); 

2. stft ix:=col(2) interval:=4; 

3. stft ix:=col(2) option:=complex; 

4. stft ix:=col(2) winlen:=32 fftlen:=64 overlap:=16; 

5. stft ix:=col(2) win:=tri; 

6. stft ix:=col(2) win:=gauss correct:=power alpha:=3; 

7. stft ix:=col(2) win:=kaiser beta:=2; 

8. stft ix:=col(2) plot:=0; 

## Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Input ix

Input

vector<complex>

<active>
Specifies the input signal
Specify By mode

Input

int

0

Option list:

• interval:Interval {0}
• freq:Frequency {1}
Sampling Interval interval

Input

double

<auto>
Specifies the sampling interval if mode is interval. The default is <auto>, which corresponds to an automatically-calculated interval.
Sampling Frequency freq

Input

double

<auto>
Specifies the sampling frequency if mode is frequency. The default is <auto>, which corresponds to an automatically-calculated frequency.
FFT Length fftlen

Input

int

256
Specifies the size of FFT section
Window length winlen

Input

int

256
Specifies the window size, which must not be greater than the size of an FFT section
Overlap overlap

Input

int

128
Specifies the number of data points by which the window sections overlap. It should be less than the window size
Window Type win

Input

int

4
Specifies the window type used by FFT

Option list:

• rect:Rectangle {0}
Rectangular window
• welch:Welch {1}
Welch window
• tri:Triangular {2}
Triangular window
• bartlett:Bartlett {3}
Bartlett window
• hanning:Hanning {4}
Hanning window
• hamming:Hamming {5}
Hamming window
• blackman:Blackman {6}
Blackman window
• gauss:Gaussian {7}
Gaussian window
• kaiser:Kaiser {8}
Kaiser window
Alpha alpha

Input

double

0
This variable is only available when Window Type is Gaussian. It specifies the Alpha parameter for Gaussian window.
Beta beta

Input

double

0
This variable is only available when Window Type is Kaiser. It specifies the Beta parameter for Kaiser window.
Window Correction correct

Input

int

amplitude

Specifies the Window Correction Factor used to correct the alteration made by applying a window to the input data.

Option list

• none:None
No correction is applied.
• amp:Amplitude
Amplitude Correction is applied.
• power:Power
Energy Correction is applied.
Option option

Input

int

2
Specifies the computation option. The default is 2, which correspond to the computing of the amplitude in dB.

Option list:

• complex:Complex Result {0}
The complex result of STFT will be computed.
• amp:Amplitude Result {1}
The amplitude of the complex result will be given
• ampdb:Amplitude in dB {2}
The amplitude in dB will be computed.
Swap Time and Frequency swapxy

Input

int

0
Specifies whether to swap the time axis and the frequency axis in the image plot.
Output Matrix om

Output

MatrixObject

[<new>]<new>!
Specify the output matrix
Create Image Plot plot

Input

int

1
Specify whether an image plot of the result will be generated
Output Worksheet rd

Output

ReportData

[<input>]<new>
Specify the output worksheet.

## Examples

1. To perform stft of Column B using the default setting:

stft ix:=col(b)

2. To perform stft with Hanning window:

stft -d

to open the dialog. Then select Hanning window for Window Type.

3. To perform stft using a pre-saved analysis theme called MyTheme, use the Command Window:

stft -t "MyTheme"

## Algorithm

stft Computation

stft is computed in the following procedure:

1. N points are taken from the input signal, where N is equal to the window size.

2. A window of the chosen type is used to multiply the extracted data, point-by-point.

3. Zeros will be padded on both sides of the window, if the window size is less than the size of the FFT section.

4. FFT is computed on the FFT section.

5. Move the window according to the user-specified overlap size, and repeat steps 1 through 4 until the end of the input signal is reached.

The Window Functions

The sliding windows are defined as follows:

Rectangular Window:

for

Welch Window:

for

Triangular Window:

$\mbox{For } 0 \le n \le N-1$

$w[n]= \begin{cases} \frac{2}{N+1}(\frac{N+1}{2}-|n-\frac{N-1}{2}|), & \mbox{if }N\mbox{ is odd} \\ \frac{2}{N}(\frac{N}{2}-|n-\frac{N-1}{2}|), & \mbox{if }N\mbox{ is even} \end{cases}$

Bartlett Window:

$w[n]=\frac{2}{N-1}(\frac{N-1}{2}-|n-\frac{N-1}{2}|) \mbox{ for } 0 \le n \le N-1$

Hanning Window:

for

Hamming Window:

for

Blackman Window:

for

Gaussian Window:

$w[n]=e^{-\frac{1}{2}(\alpha\frac{n-(N-1)/2}{(N-1)/2})^2} \mbox{ for } 0 \le n \le N-1$

Kaiser Window:

$w[n]=\frac{I(\beta\sqrt{1-(\frac{2n}{N-1}-1)^2})}{I(\beta)} \mbox{ for } 0 \le n \le N-1$

where I(ix) denotes Bessel Function.

Computation of the Sampling Interval

For details of the auto computation of the sampling interval, please see the X-Function document for fft1.