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16COMPARISON OF FILTERS WITH FINITE PULSE CHARACTERISTICS AND INFINITE PULSE CHARACTERISTICS IN MATLAB
Mokhirakhon Kurbonalievna Khusanova
Lecturer, Fergana branch of TUIT named after Muhammad Al-Khorazmiy
ABSTRACT
Digital systems are systems with digital input and output signals. Their core is usually a digital computer. Humanity has created a small number of digital objects, so the general term digital system is rarely used. The terms digital filter or digital control system are very common and they clearly reflect the main application of these systems. Often a digital control system is also called a digital filter. Thus, the digital filter is a discrete time system, the output of which is a modified version of the input.
Keywords: ICT, innovation, digital filter, digital computer, MATLAB, correlation, continuous signal, internet, control system.
INTRODUCTION
Filters are the backbone of many signal processing programs. Typical use is to isolate or limit an input signal or a region of a specific frequency spectrum. Filters used to transform a signal are often referred to as frequency selective filters because they are usually designed based on frequency response requirements.
The term "digital filter" refers to a device that implements a mathematical algorithm using hardware or software, in which the input signal is a digital signal and the output signal receives another digital signal. In this case, the amplitude and phase characteristics of the digital filter will have a special shape[1]. In many cases, the use of digital filters has the advantage that they provide relatively accurate amplitude and phase response values.
LITERATURE REVIEW
Digital filters are divided into two main types:
- filters with finite impulse response;
- filters with infinite impulse response.
One of the main important features of finite impulse response filters is that they can achieve a very linear phase response. When a signal passes through a digital filter, its amplitude and / or phase changes. The cause and magnitude of the signal change depends on the amplitude and phase characteristics of the filter. One of the convenient types of estimating the magnitude of the phase change is the phase or group delay of the signal. If the signal spectrum consists of several frequencies (for example, audio and modulated signals), the phase delay of the filter is the value of the delay during this time, which is the delay in the passage of each spectral component of the signal through
the filter. Group delay is the average time delay of the components of the signal spectrum[2].
A filter with a non-linear phase response changes (distorts) the phase of the signal passing through it. In this case, the components of the signal spectrum change to values that are not proportional to their frequencies, which leads to a change in the harmonic connections (phases) between them. To prevent such interference, it is necessary to use line filters with phase characteristics in the frequency range where the signal spectrum is located (for example, when transferring data, listening to music, watching videos, and in biomedicine there are special requirements for the characteristics of line filters).
IIR filters can be calculated in the frequency and time domains. Frequency domain calculation uses analog and digital prototype synthesis. Numerical calculation methods designed for frequency and time domains[3].
DISCUSSION
The advantage of an infinite impulse response filter is the flexibility achieved through feedback. For example, the design of infinite impulse response filters usually requires fewer coefficients than limited impulse response filters to meet the same specifications, so in cases where the frequency response of the impulse response between infinite filters is small, that is, the transient part of the frequency response is used, when the slope should be steep.
Let's use the Filter Design APP in MATLAB to filter a noisy music file. First, let's load the audio data. Let's do it just by double-clicking on the mp3 files. Leave the variable names as default. In the initial state, the input signal (Debussy) is noisy. Let's look at this signal in the time domain in the Signal Analyzer application.
Let's add a sampling rate to it to observe the signal in real seconds and hertz. And display its spectrum on the display tab, the Spectrum button. The cursor will help you understand where the border of the useful signal and noise lies. The border is located in the region of 2.2 kilohertz.
Figure 2. Spectrum display Let's open the Filter Designer application. Let's try to develop a suitable digital filter in it.
Figure 3. Design Filter Page 294
Here we select the response type, leave it Lawpass, this is a low-pass filter. Let's try to implement the equripple FIR filter, specify the sampling rate, also set our half-fence bandwidth limits to 2200 and 2400, set ripple 01 and click Design Filter.
We observe the frequency response, the shape is quite consistent with the specification. The phase of the frequency characteristics turns out to be linear in the passband. The group phase delay is constant and we can immediately estimate the shape of the impulse response and the transient function.
On the information tab, we can see that the filter requires a lot of resources, more than seven hundred multipliers, adders and registers.
RESULTS
Let's check if the IIR filter will be more economical. Let's choose the most economical elliptical IIR filter. We observe the shape of its frequency response and in the information we see that this filter requires 30 times less resources. This is a big difference.
But you will have to pay for it with phase nonlinearity, as well as frequency-dependent group and phase delays. But our IIR filter is stable, that is, all its poles are inside a circle of unit radius, as can be seen on the zero-pole diagram.
And in the information about the filter structure, we see the inscription Second Order Sections. Let's show the structure in the middle of the second-order sections documentation - this is a cascading way of constructing without filters from a smaller second-order filter.
Let's leave everything as it is. Let's make sure the shape of the frequency response suits us, and the phase for the task of filtering audio is not so critical. We now export the calculated filter coefficients to the MATLAB workspace, as a so-called SOS matrix and a vector of gains for each stage.
Figure 4. Export computed filter coefficients to MATLAB Workspace
Each section contains 6 coefficients, they are combined into an n by 6 matrix. If desired, we can transform this form of representation into the coefficients of the transfer function familiar to us.
Let's use the sos2tf function and get the common fraction for the whole filter. Now let's filter the data input signal and evaluate the spectrum in Signal Analyzer.
Figure 5. Spectrum display
Add a vector y, indicate the sampling rate so that it can be drawn on the time axis. We indicate here Sample Rate and Start Time fs, and we observe that the amplitude has clearly decreased over the entire time interval. But even on the spectrum after 2.2 kilohertz, we observe serious suppression.
Figure 6. Filter output with sound command
Now let's check if we managed to free Debussy from this hindrance. Let's listen to the filter output with the sound command. Overall it worked out well.
CONCLUSION
In conclusion, we can say that the Filter Design APP, included in the Matlab program, can be used as an optimal method for choosing one of the filters with a finite impulse response and an infinite impulse response in digital signal processing.
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