National Instruments 320571-01 用户手册

The discrete implementation of the DFT is a numerically intense process.  However, it is possible to implement a
fast algorithm when the size of the sequence is a power of two.  These algorithms are known as FFTs, and can be
found in many introductory digital signal processing (DSP) texts.

The resulting complex FFT sequence has the conventional DSP format as described in this section.

If there are n number of elements in the complex sequence and k = n/2, then the output of the FFT is organized as
follows:

Y[0]

DC component

Y[1]

Positive first harmonic

Y[2]

Positive second harmonic

   :

:

Y[k-1]

Positive k-1 harmonic

Y[k]

Nyquist frequency

Y[k+1]

Negative k-1 harmonic

   :

:

Y[n-2]

Negative second harmonic

Y[n-1]

Negative first harmonic

The following conventions and restrictions apply to the VIs in the Frequency Domain folder:

•

All arrays must be a power of two:  n = 2

m

,  m = 1, 2, 3, …, 24 (limited by onboard memory).

•

Complex sequences are manipulated using two arrays.  One array represents the real elements.  The other array
represents the imaginary elements.

The following notation is used to describe the FFT operations performed in the Frequency Domain class:

•

Y = FFT {X}, the sequence Y is the FFT of the sequence X.

•

Y = FFT

-1

 {X}, the sequence Y is the inverse FFT of the sequence X.

X is usually a complex array but can be treated as a real array.

All of the VIs in the Filters group are digital filters that can be represented by the computational algorithm that best
describes the relationship between the input and output discrete time sequences.  This computational algorithm is
referred to as the Linear Constant Coefficient Difference Equation.  This equation relates the input and output by the
basic operations of addition, delay and multiplication.  The following equation relates the input and output
sequences x and y, respectively at the discrete time instant n:

i = N-1

i = M-1

a(0)*y(n) =

∑

 (x[n-i]*b(i)) - 

∑

 (y[n-i]*a(i))

(a)

i = 0

i = 1

where :

x

is the discrete time input signal to the system represented by the filter

y 

is the discrete time output signal of the system represented by the filter

a 

is the set of coefficients applied to the input in the linear difference equation and represent the
multiplication factors for delays.  The equation suggests that there are N such coefficients.

b 

is the set of coefficients applied to the output in the linear difference equation and represent the
multiplication factors for delays.  The equation suggests that there are M such coefficients.