FFT (Not in Base Package)

Computes the fast Fourier transform (FFT) of the input sequence X. You can use this polymorphic VI to compute the FFT for a real signal or a complex signal. The data type you wire to the X input determines the polymorphic instance to use. Details  

Real FFT

	X is the real input sequence.
	FFT {X} is the FFT of X.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Complex FFT

	X is the complex valued input signal.
	FFT {X} is the FFT of X.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

FFT Details

Real FFT

The input sequence is real-valued.

The Real FFT VI executes fast radix-2 FFT routines if the size of the input sequence is a valid power of 2

size = 2^m.

m = 1, 2,…, 23.

If the size of the input sequence is not a power of 2 but is factorable as the product of small prime numbers, the VI uses a mixed radix Cooley-Tukey algorithm to efficiently compute the DFT of the input sequence.

Refer to the Fast FFT Sizes section of Chapter 4, Frequency Analysis in the LabVIEW Analysis Concepts manual for more information about fast FFT input sequence sizes.

The output sequence Y = Real FFT[X] is complex and returns in one complex array

Y = YRe + jYIm

Complex FFT

If Y represents the complex output sequence, then

Y = F{X}

You can use the Complex FFT VI to perform the FFT and the DFT of the complex-valued sequence X.

The Complex FFT VI first analyzes the input data, and based on this analysis, the VI calculates the Fourier transform of the data by executing one of the preceding options. All these routines take advantage of the concurrent processing capabilities of the CPU and FPU.

When the number of samples in the input sequence X is a valid power of 2,

n = 2^m,

for m = 1, 2, 3, …23,

where n is the number of samples. The Complex FFT VI computes the fast Fourier transform by applying a fast radix-2 FFT algorithm.

When the number of samples in the input sequence X is not a valid power of 2 but is factorable as the product of small prime numbers, the Complex FFT VI computes the discrete Fourier transform by using an efficient DFT algorithm. The largest complex DFT that can be computed is

2²² – 1 = 4,194,303 (4M – 1)

Refer to the Fast FFT Sizes section of Chapter 4, Frequency Analysis in the LabVIEW Analysis Concepts manual for more information about fast FFT input sequence sizes.

Let Y be the complex output sequence and n be the number of samples in it. You can show that

,

which means you can interpret the (n – 1)^th element of Y as the –i^th element of the sequence, if it could be physically realized, which represents the FFT value corresponding to frequency If.

If n is even, let k = n/2. The following table shows the format of the complex output sequence.

Array Element	Corresponding Frequency
Y0	DC component
Y1	f
Y2	2f
Y3	3f
Yk – 2	(k – 2)f
Yk – 1	(k – 1)f
Yk	Nyquist Frequency
Yk + 1 = Yn – (k – 1) = Y – (k – 1)	–(k – 1)f
Yk + 2 = Yn –(k – 2) = Y –(k – 2)	–(k – 2)f
Yn – 3	–3f
Yn – 2	–2f
Yn – 1	–f

The following illustration represents this complex sequence.

If n is odd, let k = (n-1)/2. The following table shows the format of the complex output sequence Y.

Array Element	Corresponding Frequency
Y0	DC component
Y1	f
Y2	2f
Y3	3f
Yk – 1	(k – 1)f
Yk	kf (Nyquist Frequency)
Yk + 1 = Yn – (k – 1) = Y –(k – 1)	–kf
Yk + 2 = Yn – (k – 2) = Y –(k – 2)	–(k – 1)f
Yn – 3	–3f
Yn – 2	–2f
Yn – 1	–f

The following illustration represents the preceding table.

This format is an accepted standard in digital signal processing applications. It is convenient because it simplifies performing the inverse transform to obtain the final, processed result.