Why do signals differ in fdesign.fracdelay and dsp.Variab​leFraction​alDelay?

Hello!

I use two Matlab functions that implement the 3rd order Farrow filter (fdesign.fracdelay and dsp.VariableFractionalDelay).

These functions give different results.

Below is a code and a graph of the absolute value of the difference of the signals at the outputs of the filters.

Why does an error occur if the coefficient must be the same?

close all;
clearvars;
clc;


%% Parameters
% Signal
fs = 2000; % Sampling  frequency
t = (0 : 1/fs : 2 - 1/fs).'; % Time
s = chirp(t-2, 4, 1/2, 6, 'quadratic', 100, 'convex').*exp(-4*(t-1).^2); % Signal

% Delay
d = 0.9;


%% FFT-delay
s_d = delayseq(s, d);

%% Farrow filter 3-rd order
fd = fdesign.fracdelay(d, 'N', 3);
cubicfarrow = design(fd, 'lagrange', 'FilterStructure', 'farrowfd');
y_farrow = filter(cubicfarrow, s);


%% Variable Fractional Delay
vfd = dsp.VariableFractionalDelay('InterpolationMethod', 'Farrow');
y_vfd = vfd(s, d);

%% Error
Err = abs(y_farrow - y_vfd);
Err_farrow = abs(s_d - y_farrow);
Err_vfd = abs(s_d - y_vfd);

%% Pots
hSig = figure ('Units',					'Normalized',			...
			  'Position',				[0.1, 0.1, 0.8, 0.8],	...
			  'PaperOrientation',		'landscape',			...
			  'NumberTitle',			'off',					...
			  'Name',					'Signal',				...
			  'Tag',					'Fig_Sig');
	movegui(hSig, 'center');
	hold on;
    ps = plot(t, s, 'Color', 'Red', 'LineWidth', 3);
	psd = plot(t, s_d, 'Color', 'Black', 'LineWidth', 3);
    psfarrow = plot(t, y_farrow, 'Color', 'Blue', 'LineWidth', 2);
    psvfd = plot(t, y_vfd, 'Color', 'Magenta', 'LineWidth', 2);
	hold off;
	grid on;
	legend([ps, psd, psfarrow, psvfd], 'Signal', 'FFT', 'fractdelay', 'VariableFractionalDelay');
    
    
hErr = figure ('Units',					'Normalized',			...
			  'Position',				[0.1, 0.1, 0.8, 0.8],	...
			  'PaperOrientation',		'landscape',			...
			  'NumberTitle',			'off',					...
			  'Name',					'Errors',				...
			  'Tag',					'Fig_Err');
	movegui(hSig, 'center');
	hold on;
    pe = plot(t, Err, 'Color', 'Red', 'LineWidth', 3);
    pefarrow = plot(t, Err_farrow, 'Color', 'Blue', 'LineWidth', 2);
    pevfd = plot(t, Err_vfd, 'Color', 'Magenta', 'LineWidth', 2);
    hold off;
	grid on;
    legend([pe, pefarrow, pevfd], '|farrow - vfd|', 'fractdelay', 'VariableFractionalDelay');

Answer 1

[Honglei Chen]

Your dsp.VariableFractionalDelay is actually order 4. If you do

vfd = dsp.VariableFractionalDelay('InterpolationMethod', 'Farrow', 'FilterLength', 3);

The result of vfd and cubicfarrow will match.

HTH

[Mikhail Yurkov]

Hello! Thanks for your reply.

But if I do

fdesign.fracdelay(d, 'N', 4);
vfd = dsp.VariableFractionalDelay('InterpolationMethod', 'Farrow', 'FilterLength', 4);

The result of vfd and cubicfarrow will not match.