Otrimannya frequency characteristics of the filter with pulse. Filter with terminal impulse response

Physically designed digital filters are processed in real time, to form an output signal at the i-th discrete moment of the hour, the following data can be used:

1. The value of the output signal at the current moment of the hour; so just a sprig of the past in the input signal: x (i-1), x (i-2), x (i-m);

2. Number of forward signals of the output signal: y (i-1), y (i-2), y (i-n).

The digits of the number m and n determine the order of the digital filter. Filters are classified according to how the information about the past of the system is scored.

Filters with FIR or NOT recursive filters, which work in the same way with the approaching algorithm.

M - filter order.

Chi is not a recursive filter vibrating sounding, summing up the forward signals of the input signal. The past few days of the exit signal are not victorious.

H (z) - system function.

The system function has m zeros and one pole, at z = 0.

The algorithm of the digital filter functioning from FIR readings is shown in Fig.45.

The main elements of the filter are blocks of fading to values ​​for 1 sampling interval.

Scale blocks, multiplied by your coefficients in digital form. From the output of large-scale blocks, the signal goes into the battery, where the output signal is calculated.

The block diagram is given not electrically, but to serve graphic images signal processing algorithm on the EOM. Arrays of numbers serve as output and input data for such an algorithm.

It is necessary to control the system functions of Z - transformation and we know the impulse response:

(Impulse response of the filter).

The impulse response of the FIR filter is to compensate for the last number of elements and data. The filter is stable.

We know the frequency response of the substitution

T = 1 / fs - sampling interval.

Filter with terminal impulse response (non-recursive filter, FIR filter) Abo FIR-filter (FIR speed. Finite impulse response - final impulse response) is one of the types of linear digital filters, a characteristic feature of which is the interchange over the hour of the yogo impulse response (at the hour of the hour, it becomes exactly equal to zero). Such a filter is also called non-recursive through the presence of a pivot link. The denominator of the transfer function of such a filter is like a constant.

dynamic characteristics

de - delta function. Then the impulse response of the FIR filter can be written as:

#define N 100 // filter order float h[N] = ( #include "f1.h"); // insert the file with the given filter coefficients floatx[N]; floaty[N]; short my_FIR(short sample_data)(float result=0; for(int i=N - 2; i>=0; i--)(x[i+1]=x[i]; y[i+1]= y[i];) x[0] = (float)sample_data;for(int k = 0;k< N; k++ ) { result = result + x[ k] * h[ k] ; } y[ 0 ] = result; return ((short ) result) ; }

Div. also

force

• Analysis of the FIR filter with a linear phase-frequency characteristic by the method of frequency vibrating

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See also "Filter with terminal impulse response" in other dictionaries:

Filter - use the BeTechno promo code for Akademika, or buy the filter with a discount at BeTechno sales

FIR filter- - Electrical communication topics, basic concepts EN finite impulse response (filter) FIR ... Dovіdnik technical translation

Recursive filter- (Recursive filter, IIR filter) or IIR filter (IIR speed. Infinite impulse response non-infinite impulse response) linear electronic filter, like a vicorist one or more of its inputs in the input quality, then ... ... Wikipedia

FIR filter

non-recursive filter- A filter with a terminal impulse response (non-recursive filter, FIR filter, FIR filter) is one of the types of linear electronic filters, a characteristic feature of which is the exchange by hour of its impulse response (from which ... Wikipedia

recursive filter- A filter with an unskinned impulse response (Recursive filter, IIR filter) is a linear electronic filter, which is one or more of its own inputs in the quality of the input, which I make Zvorotniy zv'azok. The main power of such filters is ... Wikipedia

digital filter- Digital filter in electronics, whether it is a filter that is processed digital signal with the method of seeing and / or smothering the singing frequencies of the signal. On the front of the digital, analog filter can be on the right of the analog signal, its power ... ... Wikipedia

discrete filter- Digital filter in electronics, be it a filter that processes a digital signal with a method of seeing and / or smothering the singing frequencies of the signal. At the top of the digital analog filter can be on the right side of the analog signal, its power is non-discrete, ... ... Wikipedia

line filter- Line filter is a dynamic system, like a stagnant one line operator to the input signal for viewing or smothering the singing frequencies of the signal and other functions by processing the input signal. Line filters are widely promoted in ... ... Wikipedia

Change middle (filter)- This term may also have other meanings of divs. Change the middle (meaning). Block diagram of a simple FIR filter of a different order, which implements the average change average, the average variation of the digital filter s ... ... Wikipedia

Change middle (value)- changing the average, moving average (eng. Moving average): changing the average of the family of functions, the value of which in the skin point is assigned to the average value of the external function for the forward period. Change of middle ... ... Wikipedia

Novosibirsk State Technical University

FACULTY OF AUTOMATICS AND NUMERICAL TECHNOLOGY

Department of Collection Systems and Data Processing

Discipline "Theory and processing of signals"

Lab robot No.10

Digital FILTERS

With terminal impulse response

Group: AT-33

Option: 1 vikladach:

student: Shadrina A.V. Assoc. Shchetinin Yu.I.

Meta robots: development of methods for analysis and synthesis of filters with terminal impulse response and smoothing of end functions.

Vikonanny roboti:

1. Graphs of the impulse response of the FIR low-pass filter with a rectoductal window with a frequency in view for the value of the filter duration i.

The impulse response of an ideal discrete FIR filter has an indefinite value and is not equal to zero for negative values:

.

In order to take away the physically adjusted filter, next encircle the impulse characteristic by the end number, and then collapse the characteristic to the right by a value.

The value is the price of the dozhina (rozmіr) of the filter, - filter order.

Matlab Script (labrab101.m)

N = input( "Enter filter length N =");

h = sin(wc.*(n-(N-1)/2)) ./(pi.*(n-(N-1)/2));

xlabel( "Number of the note, n")

>>subplot(2,1,1)

>>labrab101

Enter filter depth N = 15

>> title ( "Impulse response of the FIR filter for N = 15")

>>subplot(2,1,2)

>>labrab101

Enter filter depth N = 50

>> title ( "Impulse response of the FIR filter for N = 50")

Fig.1. Graphs of the impulse response of the FIR low-pass filter with a rectangular window with a frequency of 3 for the value of the filter duration i

comment: How to look at the frequency response of a digital filter like the Four's series: , Then the coefficient of the row will be the value of the impulse response of the filter. In this case, the Four's series was shortened in the first case to, and in the other - to, and then the characteristics were truncated along the direction of the axis to the right to remove the causal filter. When the width of the head flute is set to 2, and when it is - 1, then when the filter height is increased, the head flute of the impulse response sounds. Well, if you look at the rіven of the pelustok (for help), then with the zbіlshennі vіn zbіlshivsya for the absolute value of z to. In this way, it is possible to make visnovoks, but with varying approximations of the ideal frequency response of the filter with a straight-width window, it is not possible to simultaneously sound the head pelus (and thereby change the transitional area) and change the equalities of the flank pelus (change the flicker in the transmission). The only parameter of a straight-cut vein is yogo rozmіr, for the help of which you can add to the width of the head cape, protege, on the side of the paddle of the vein, do not rob a special injection.

2. Calculation of the DTFT of impulse characteristics from item 1 for an additional function. Graphs of their frequency response in a linear scale and in decibels for 512 vіdlіkіv frequency. Smuga passing through, transitional smuga and smuga zatrimuvannya filter. Having added the order of the filter to the width of the transitional smog and the frequency response ripples in the smogs of transmission and trimming.

Matlab Function (DTFT.m)

function = DTFT(x, M)

N = max(M, length(x));

% Reduced FFT to 2 ^ m

N = 2^(ceil(log(N)/log(2)));

% Calculated fft

% Frequency vector

w = 2 * pi * ((0: (N-1)) / N);

w = w - 2 * pi * (w >= pi);

% FFT failure up to interval vіd -pi to + pi

X=fftshift(X);

w = fftshift(w);

Matlab Script (labrab102.m)

h1 = sin(wc.*(n1-(N1-1)/2)) ./(pi.*(n1-(N1-1)/2));

h2 = sin(wc.*(n2-(N2-1)/2)) ./(pi.*(n2-(N2-1)/2));

DTFT(h1.512);

DTFT(h2.512);

plot(w ./(2*pi), abs(H1) ./ max(abs(H1)), "r")

xlabel("f, hz"), ylabel("|H1|/max(|H1|)"), grid

plot(w./(2*pi), abs(H2) ./ max(abs(H2)), "b")

xlabel("f, hz"), ylabel("|H2|/max(|H2|)"), grid

plot(w./(2*pi), 20*log10(abs(H1)), "r")

title ( "Frequency response of the FIR low-pass filter with a rectangular window for N = 15")

xlabel("f, Hz"), ylabel("20lg(| H1|), dB"), grid

plot(w./(2*pi), 20*log10(abs(H2)), "b")

title ( "Frequency response of the FIR low-pass filter with a rectangular window for N = 50")

xlabel("f, Hz"), ylabel("20lg(| H2|), dB"), grid

Fig.2. Graphs of the frequency response of the FIR low-pass filter with a recto-wave window frequency in terms of the value of the filter pressure and in a linear scale

Fig.3. Graphs of the frequency response of the FIR low-pass filter with a recto-wave window frequency in terms of the value of the filter pressure and in a logarithmic scale

comment:

Table 1

dozhina filter	Smuha transmission, Hz	Transition area, Hz	Smuga zatrimuvannya, Hz
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