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36USING DECIMATION AND INTERPOLATION WHEN PROCESSING
SIGNALS IN MATLAB
Mokhirakhon Kurbonalievna Khusanova
Lecturer, Fergana branch of TUIT named after Muhammad Al-Khorazmiy
ABSTRACT
The increasing demands of time on digital filters require the creation of digital processing filters for discrete signals with different rates, capable of digital processing of signals with different sampling rates. This processing of discrete signals uses the following two operations: decimation and interpolation, which provide an efficient sequential implementation of different transmission rates. Decimation lowers the sample rate by compressing it while retaining the information in the signal. As a result of interpolation, the inverse sampling rate is increased.
Keywords: innovation, discrete convolution, Matlab, correlation, impulse response, continuous signal, discrete signal, sequences.
INTRODUCTION
In the field of audio signal processing, multi-rate processing ensures that the size of the storage device needed to store it is small or that the transmission rate is reduced. Providing relatively inexpensive, high-resolution analog-digital conversion to digital audio signals required a switch to fallback sampling instead of the traditional sequential approach.[1]
Signal processing at different speeds provides efficient implementation of digital signal processing function. For example, implementing digital narrowband finite impulse response filtering using conventional DSP poses several noteworthy problems because such filters require multiple coefficients to be computed to meet stringent frequency response requirements.
The method of processing signals at different rates makes filtering very effective at much lower rates, resulting in a much lower filtering order.[2]
LITERATURE REVIEW
The easiest and easiest way to reduce the sampling rate of a digital signal is to return it to its original analog form and resample it at a different rate. However, the digital-analog conversion process has the following disadvantages: quantization and assembly errors result in significant waveform distortion. Therefore, if the signal is supplied in digital form, it is preferable to process it based on the digital method. Digital Processing at Multiple Rates - Effectively altering the sampling rate of a signal based on a digital technique that uses traditional digital signal processing techniques. For example, DSP can be performed digitally in real time to reduce signal overlap and
reduce the effect of reflection frequency, resulting in dramatic increases in filter slope and phase linearity.
Decimation is a decrease in the sampling frequency of a time-discrete signal by decimating its samples.
Interpolation is the digital equivalent of analog-to-digital conversion, in which the analog signal is reconstructed using interpolation from digital instantaneous values assigned to the input of the digital-to-analog converter.[3]
DISCUSSION
A digital filter converter is used to eliminate signal overlap or reverse frequency loss. The processing speed of signals at different speeds depends on the type and quality of the filter used. Decimation and interpolation can use infinite and finite impulse response filters, but finite impulse response filters are often used.
Downsampling rate.
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Figure 1. Downsampling rate
Consider an example of lowering the frequency of signals in Matlab. In this script, we first form the original signal of the sum of two harmonic signals with frequencies of 1000 Hz and 3400 Hz. And then we downsample the sampling rate by an integer number of times. Original sampling rate FS = 30,000 Hz. Let's look at the signal in the time and frequency domains, and also listen.
On the signal spectrum, we observe clear peaks at 1000 and 3400 Hz.
Now our task is to lower the sampling rate. We will do it three times by a factor of down = 3 and first we will downsample the sample rate using the downsample method, and then with the decimate command.
There is no difference by ear, the time counts do not differ. Aspects peaks at 1000 and 3400 Hz. We downsampled to ten kilohertz.
Figure 2. Downsampling rate
The nyquest zone, that is, the sampling rate in half in our case is limited to five kilohertz. But what happens if you lower the sampling rate by six times. The zone is nyquest, and it moves 2.5 kilohertz, what happens to the 3400 signal? The aliasing effect transforms it into a 1600 Hz signal.
We observe non-observance of the Kotelnikov theorem both on the signal spectrum and when listening. But the decimate command pre-filters the signal.
Thus, only those signals whose frequency does not exceed half the sampling frequency of the output signal fall into the resulting nyquest zone, and we will hear a pure tone of 1000 hertz.
Upsampling rate.
Figure 3. Upsampling rate
RESULTS
Now let's look at some examples of upsampling a harmonic signal in Live Script. Original sine wave signal with a fundamental frequency of 1000 hertz and a sampling rate of 8000 hertz. Let's look at it in the time and frequency domains, and also listen to. On the spectrum, we observe one clear peak in the region of 1000 hertz, and the observation area of the spectrum is limited to 4 kilohertz.
Now let's raise the sample rate by three times using the upsample method. Zeros will appear between the signal samples and the sound will be distorted. But the most interesting thing we see on the signal spectrum. And by raising the sampling rate, we expanded the nyquest zone three times. Now the spectrum contains frequencies from 0 to 12 kilohertz and we clearly observe spectral copies at frequencies of 7 and 9 kilohertz. The spectrum is mirrored in a band of 8 kilohertz and repeats with a period of 8 kilohertz. This is exactly the value of our sample rate. The resulting spectral copies give us three audio tones that distort our audio.
Now let's look at the repeat method, repeating reports also distorts the shape of the sine wave. But less so than adding zeros.
CONCLUSION
The signal is a little more like a 1 kilohertz tone, in the time domain it has fewer sharp drops and spectral copies at 7 and 9 kilohertz are shown to be suppressed relative
to one kilohertz. But the only way to get one tone at an increased sampling rate is by interpolation. It will allow us to get approximate values between real reports of the input signal, but the shape of the interpolated sinusoid does not look distorted. We observe one peak on the spectrum and the signal is indistinguishable from the initial one by ear..
An interpolation process must always be performed before decimation, otherwise some frequency components may be lost due to decimation.
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