dsp.HDLIFFT
Inverse fast Fourier transform — optimized for HDL code generation
Description
The HDL IFFT System object™ provides two architectures to optimize either throughput or area. Use the streaming Radix 2^2 architecture for high-throughput applications. This architecture supports scalar or vector input data. You can achieve giga-sample-per-second (GSPS) throughput using vector input. Use the burst Radix 2 architecture for a minimum resource implementation, especially with large FFT sizes. Your system must be able to tolerate bursty data and higher latency. This architecture supports only scalar input data. The object accepts real or complex data, provides hardware-friendly control signals, and has optional output frame control signals.
To calculate the inverse fast Fourier transform:
Create the
dsp.HDLIFFTobject and set its properties.Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?.
Creation
Description
IFFT_N = dsp.HDLIFFTIFFT_N, that performs a fast Fourier transform.
IFFT_N = dsp.HDLIFFT(Name,Value)
ifft128 = dsp.HDLIFFT('FFTLength',128)Properties
Usage
Syntax
Description
[
returns the inverse fast Fourier transform (IFFT) when using the burst Radix 2
architecture. The Y,validOut,ready]
= IFFT_N(X,validIn)ready signal indicates when the object can accept
input samples.
To use this syntax, set the Architecture
property to 'Burst Radix 2'. For example:
IFFT_N = dsp.HDLIFFT(___,'Architecture','Burst Radix 2'); ... [y,validOut,ready] = IFFT_N(x,validIn)
[
also returns frame control signals Y,startOut,endOut,validOut]
= IFFT_N(X,validIn)startOut and
endOut. startOut is true on
the first sample of a frame of output data. endOut is
true for the last sample of a frame of output data.
To use this syntax, set the StartOutputPort
and EndOutputPort
properties to true. For example:
IFFT_N = dsp.HDLIFFT(___,'StartOutputPort',true,'EndOutputPort',true); ... [y,startOut,endOut,validOut] = IFFT_N(x,validIn)
[
returns the IFFT, Y,validOut]
= IFFT_N(X,validIn,resetIn)Y, when validIn is
true and resetIn is false.
When resetIn is true, the object stops the current
calculation and clears all internal state.
To use this syntax, set the ResetInputPort
property to true. For example:
IFFT_N = dsp.HDLIFFT(___,'ResetInputPort',true); ... [y,validOut] = IFFT_N(x,validIn,resetIn)
Input Arguments
Output Arguments
Object Functions
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj, use
this syntax:
release(obj)
Examples
Create IFFT for HDL Code Generation
Create the specifications and input signal. This example uses a 128-point FFT.
N = 128;
Fs = 40;
t = (0:N-1)'/Fs;
x = sin(2*pi*15*t) + 0.75*cos(2*pi*10*t);
y = x + .25*randn(size(x));
y_fixed = sfi(y,32,16);
noOp = zeros(1,'like',y_fixed);
Compute the FFT of the signal to use as the input to the IFFT object.
Note: This object syntax runs only in R2016b or later. If you are using an earlier release, replace each call of an object with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).
hdlfft = dsp.HDLFFT('FFTLength',N,'BitReversedOutput',false); Yf = zeros(1,4*N); validOut = false(1,4*N); for loop = 1:1:N [Yf(loop),validOut(loop)] = hdlfft(complex(y_fixed(loop)),true); end for loop = N+1:1:4*N [Yf(loop),validOut(loop)] = hdlfft(complex(noOp),false); end Yf = Yf(validOut == 1);
Plot the single-sided amplitude spectrum.
plot(Fs/2*linspace(0,1,N/2),2*abs(Yf(1:N/2)/N)) title('Single-Sided Amplitude Spectrum of Noisy Signal y(t)') xlabel('Frequency (Hz)') ylabel('Output of FFT (f)')
Select frequencies that hold the majority of the energy in the signal. The cumsum function does not accept fixed-point arguments, so convert the data back to double.
[Ysort,i] = sort(abs(double(transpose(Yf(1:N)))),1,'descend'); Ysort_d = double(Ysort); CumEnergy = sqrt(cumsum(Ysort_d.^2))/norm(Ysort_d); j = find(CumEnergy > 0.9, 1); disp(['Number of FFT coefficients that represent 90% of the ', ... 'total energy in the sequence: ', num2str(j)]) Yin = zeros(N,1); Yin(i(1:j)) = Yf(i(1:j));
Number of FFT coefficients that represent 90% of the total energy in the sequence: 4
Write a function that creates and calls the IFFT System object™. You can generate HDL from this function.
function [yOut,validOut] = HDLIFFT128(yIn,validIn) %HDLIFFT128 % Processes one sample of data using the dsp.HDLIFFT System object(TM) % yIn is a fixed-point scalar or column vector. % validIn is a logical scalar. % You can generate HDL code from this function. persistent ifft128; if isempty(ifft128) ifft128 = dsp.HDLIFFT('FFTLength',128); end [yOut,validOut] = ifft128(yIn,validIn); end
Compute the IFFT by calling the function for each data sample.
Xt = zeros(1,3*N); validOut = false(1,3*N); for loop = 1:1:N [Xt(loop),validOut(loop)] = HDLIFFT128(complex(Yin(loop)),true); end for loop = N+1:1:3*N [Xt(loop),validOut(loop)] = HDLIFFT128(complex(0),false); end
Discard invalid output samples. Then inspect the output and compare it with the input signal. The original input is in green.
Xt = Xt(validOut==1);
Xt = bitrevorder(Xt);
norm(x-transpose(Xt(1:N)))
figure
stem(real(Xt))
figure
stem(real(x),'--g')
ans =
0.7863
Create a Vector-Input IFFT for HDL Code Generation
Create the specifications and input signal. This example uses a 128-point FFT and computes the transform over 16 samples at a time.
N = 128; V = 16; Fs = 40; t = (0:N-1)'/Fs; x = sin(2*pi*15*t) + 0.75*cos(2*pi*10*t); y = x + .25*randn(size(x)); y_fixed = sfi(y,32,24); y_vect = reshape(y_fixed,V,N/V);
Compute the FFT of the signal, to use as the input to the IFFT object.
Note: This object syntax runs only in R2016b or later. If you are using an earlier release, replace each call of an object with the equivalent step syntax. For example, replace myObject(x) with step(myObject,x).
hdlfft = dsp.HDLFFT('FFTLength',N); loopCount = getLatency(hdlfft,N,V)+N/V; Yf = zeros(V,loopCount); validOut = false(V,loopCount); for loop = 1:1:loopCount if ( mod(loop,N/V) == 0 ) i = N/V; else i = mod(loop,N/V); end [Yf(:,loop),validOut(loop)] = hdlfft(complex(y_vect(:,i)),(loop<=N/V)); end
Plot the single-sided amplitude spectrum.
C = Yf(:,validOut==1); Yf_flat = C(:); Yr = bitrevorder(Yf_flat); plot(Fs/2*linspace(0,1,N/2),2*abs(Yr(1:N/2)/N)) title('Single-Sided Amplitude Spectrum of Noisy Signal y(t)') xlabel('Frequency (Hz)') ylabel('Output of FFT(f)')
Select frequencies that hold the majority of the energy in the signal. The cumsum function doesn't accept fixed-point arguments, so convert the data back to double.
[Ysort,i] = sort(abs(double(Yr(1:N))),1,'descend'); CumEnergy = sqrt(cumsum(Ysort.^2))/norm(Ysort); j = find(CumEnergy > 0.9, 1); disp(['Number of FFT coefficients that represent 90% of the ', ... 'total energy in the sequence: ', num2str(j)]) Yin = zeros(N,1); Yin(i(1:j)) = Yr(i(1:j)); YinVect = reshape(Yin,V,N/V);
Number of FFT coefficients that represent 90% of the total energy in the sequence: 4
Write a function that creates and calls the IFFT System object™. You can generate HDL from this function.
function [yOut,validOut] = HDLIFFT128V16(yIn,validIn) %HDLFFT128V16 % Processes 16-sample vectors of FFT data % yIn is a fixed-point column vector. % validIn is a logical scalar value. % You can generate HDL code from this function. persistent ifft128v16; if isempty(ifft128v16) ifft128v16 = dsp.HDLIFFT('FFTLength',128) end [yOut,validOut] = ifft128v16(yIn,validIn); end
Compute the IFFT by calling the function for each data sample.
Xt = zeros(V,loopCount); validOut = false(V,loopCount); for loop = 1:1:loopCount if ( mod(loop,N/V) == 0 ) i = N/V; else i = mod(loop,N/V); end [Xt(:,loop),validOut(loop)] = HDLIFFT128V16(complex(YinVect(:,i)),(loop<=N/V)); end
ifft128v16 =
dsp.HDLIFFT with properties:
FFTLength: 128
Architecture: 'Streaming Radix 2^2'
ComplexMultiplication: 'Use 4 multipliers and 2 adders'
BitReversedOutput: true
BitReversedInput: false
Normalize: true
Use get to show all properties
Discard invalid output samples. Then inspect the output and compare it with the input signal. The original input is in green.
C = Xt(:,validOut==1);
Xt = C(:);
Xt = bitrevorder(Xt);
norm(x-Xt(1:N))
figure
stem(real(Xt))
figure
stem(real(x),'--g')
ans =
0.7863
Explore Latency of HDL IFFT Object
The latency of the object varies with the FFT length and the vector size. Use the getLatency function to find the latency of a particular configuration. The latency is the number of cycles between the first valid input and the first valid output, assuming that the input is contiguous.
Create a new dsp.HDLIFFT object and request the latency.
hdlifft = dsp.HDLIFFT('FFTLength',512);
L512 = getLatency(hdlifft)L512 = 599
Request hypothetical latency information about a similar object with a different FFT length. The properties of the original object do not change. When you do not specify a vector length, the function assumes scalar input data.
L256 = getLatency(hdlifft,256)
L256 = 329
N = hdlifft.FFTLength
N = 512
Request hypothetical latency information of a similar object that accepts eight-sample vector input.
L256v8 = getLatency(hdlifft,256,8)
L256v8 = 93
Enable scaling at each stage of the IFFT. The latency does not change.
hdlifft.Normalize = true; L512n = getLatency(hdlifft)
L512n = 599
Request the same output order as the input order. This setting increases the latency because the object must collect the output before reordering.
hdlifft.BitReversedOutput = false; L512r = getLatency(hdlifft)
L512r = 1078
Algorithms
Streaming Radix 2^2
The streaming Radix 2^2 architecture implements a low-latency architecture. It saves resources compared to a streaming Radix 2 implementation by factoring and grouping the FFT equation. The architecture has log4(N) stages. Each stage contains two single-path delay feedback (SDF) butterflies with memory controllers. When you use vector input, each stage operates on fewer input samples, so some stages reduce to a simple butterfly, without SDF.
The first SDF stage is a regular butterfly. The second stage multiplies the outputs of the first stage by –j. To avoid a hardware multiplier, the block swaps the real and imaginary parts of the inputs, and again swaps the imaginary parts of the resulting outputs. Each stage rounds the result of the twiddle factor multiplication to the input word length. The twiddle factors have two integer bits, and the rest of the bits are used for fractional bits. The twiddle factors have the same bit width as the input data, WL. The twiddle factors have two integer bits, and WL-2 fractional bits.
If you enable scaling, the algorithm divides the result of each butterfly stage by 2. Scaling at each stage avoids overflow, keeps the word length the same as the input, and results in an overall scale factor of 1/N. If scaling is disabled, the algorithm avoids overflow by increasing the word length by 1 bit at each stage. The diagram shows the butterflies and internal word lengths of each stage, not including the memory.
Burst Radix 2
The burst Radix 2 architecture implements the FFT by using a single complex butterfly multiplier. The algorithm cannot start until it has stored the entire input frame, and it cannot accept the next frame until computations are complete. The output ready port indicates when the algorithm is ready for new data. The diagram shows the burst architecture, with pipeline registers.
Control Signals
The algorithm processes input data only when the input valid port is 1. Output data is valid only when the output valid port is 1.
When the optional input reset port is 1, the algorithm stops the current calculation and clears all internal states. The algorithm begins new calculations when reset port is 0 and the input valid port starts a new frame.
This diagram shows the input and output valid port values for contiguous scalar input data, streaming Radix 2^2 architecture, an FFT length of 1024, and a vector size of 16.
The diagram also shows the optional start and end port values that indicate frame boundaries. If you enable the start port, the start port value pulses for one cycle with the first valid output of the frame. If you enable the end port, the start port value pulses for one cycle with the last valid output of the frame.
If you apply continuous input frames, the output will also be continuous after the initial latency.
The input valid port can be noncontiguous. Data accompanied by an input valid port is processed as it arrives, and the resulting data is stored until a frame is filled. Then the algorithm returns contiguous output samples in a frame of N (FFT length) cycles. This diagram shows noncontiguous input and contiguous output for an FFT length of 512 and a vector size of 16.
When you use the burst architecture, you cannot provide the next frame of input data until memory space is available. The ready port indicates when the algorithm can accept new input data.
Latency
The latency varies with the FFT length and the vector size. Use the getLatency
function to find the latency of a particular configuration. The latency is the number of
cycles between the first valid input and the first valid output, assuming that the input is
contiguous.
When using the burst architecture with a contiguous input, if your design waits for
ready to output 0 before de-asserting the input
valid, then one extra cycle of data arrives at the input. This data
sample is the first sample of the next frame. The algorithm can save one sample while
processing the current frame. Due to this one sample advance, the observed latency of the
later frames (from input valid to output valid) is
one cycle shorter than the reported latency. The latency is measured from the first cycle,
when input valid is 1 to the first cycle when output
valid is 1. The number of cycles between when
ready port is 0 and the output valid port is 1
is always latency – FFTLength.
