Report 3: Interference tone supression PDF

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Report completo sobre la ultima practica que se hace con el matlab en laboratorio...

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Interfering Tone Supression Sahara Gandarillas y Akram Laoulidi

Abstract: In this last laboratory session our goal is learnt to work with signals with interference and apply all the knowledge we have gained in the semester and use the theory to move more practical space and design a filter that allow us to eliminate an interfering tone of a signal, using the help of MATLAB I.

INTRODUCTION

Our goal, as mentioned before, is to create a filter with which we can suppress the interfering tone of our signal and obtain as a result our clean signal without interference. In this case we have a signal with an interference frequency fs equal to 30000 Hz. II.

BACKGROUND STUDY

Considering the objective of this practice, in order to eliminate the interfering tone, we have to create an eliminated band filter, as this type of filter will allow us to eliminate only the frequency, we are interested in. Another point to consider is the type of response we want our filter to have, that is: if it will be FIR or IIR type. In this case we will work with both. In case our filter has a FIR type response we will have the following function and diagram:

Figure 2. Zero-pole diagram IIR

𝐻(𝑧) = 𝐾

(𝑧 − 𝑒 −𝑖Ω)(𝑧 − 𝑒 𝑖Ω) (𝑧 − 𝜌𝑒 −𝑖Ω)(𝑧 − 𝜌𝑒 𝑖Ω )

Where the value of ρ determines that our system is of type IR and whose values must be 0 < ρ < 1. In this case, to plot the graph, we have assumed that the value of ρ= 0.1. he amplitude and phase shift graphs for both FIR and IR systems are the same, since the value of the zeros, which determine the elimination of a frequency, are the same in both types of system. Therefore, we obtain the following amplitude and phase shift graph for the two cases:

Figure 1. Zero-pole diagram FIR

𝐻(𝑧) = 𝐾

(𝑧 − 𝑒 −𝑖Ω)(𝑧 − 𝑒 𝑖Ω) 𝑧2

In the case that our filter has an impulse response of type IIR we will have:

Figure 3. Frequency response of the filter FIR

signal with interference, a parameter with which we determine the type of impulse response that we want our filter to have and the value of the frequency of the signal. This parameter can only take values 0 < r < 1 for it to be stable. In this case the value that we will put to this parameter will be 0 and 0.7, so our system will have an impulse response that will be FIR and IIR.

Figure 4. Frequency response of the filter IIR (𝜌= 0.7)

III.

LABORATORY WORK

Initially, we have a song whose signal, both in time and frequency representation, shows that it has an interfering tone that affects it when it is played back.

Figure 5. Plot x Figure 7. Function filtre_to_interferent

Initially, to limit our filter to the number of total samples, what we do is to define a parameter N with which, now of making the TFD, it is limited to the number of samples of the signal. We pass the signal to the frequency domain, since to make the denominator and numerator of our signal meet the requirements to be able to eliminate the frequencies we are interested in, we must work in this domain.

Figure 6. Plot of the modulus of the FFT

To eliminate this interference using Matlab as a tool, we create a function called Filter_to_inteference with which we can remove the interfering tone from our signal. As we can see in the code of the function, it has an output parameter and three inputs, in which we introduce the

Once our frequency domain signal has been defined, the next step is to define the value of the roots for both the numerator and the denominator. The numerator, considering that it is the one that defines the frequencies to be eliminated, we make the value of its root equal to the value of omega. To do this we determine the value of the position in which the interference is found

and find the value of omega, obtaining in this case that the position is 41944 and omega 0.2511.

In the case of r = 0.7 we get:

Figure 8. Numerator Polynomial

As for the value of the denominator, considering that it defines the type of impulsional response that our system will have, we define it in the same way as the numerator, but multiplied by a parameter r that will take values between 0 and 1, which will define the type of impulsional response of the system.

Figure 9. Denominator Polynomial

We then obtain the pole-zero graph and the displacement graphs to verify that the roots have been put correctly.

Figure 12. Zero-pole diagram

For r=0, the case of an FIR system, we get that:

Figure 13. Frequency response of the filter Figure 10. Zero-pole diagram

And we can see that the poles and zeros are correctly arranged. Also, if we make a comparison of both types of systems, we can see that the IIR system compared to the FIR system in terms of the magnitude graph tends more to the ideal case and is less variable than the FIR case Once we have defined the polynomials that will form the function of our filter, we define a variable h that will be for our filter. With the Matlab tools we join both polynomials defined above and limit our function to 50 samples.

Figure 11. Frequency response of the filter

Figure 14. Expression of the filter

And for the case of the IR filter we get:

Figure 15. Response filter graph (r = 0) Figure 18. Plot of the output and input signal (r = 0.7)

IV.

CONCLUSION

In conclusion, this report shows what should be done to remove an annoying beep from a song with the least amount of error. It is also proven how the different types of filters work, with the high modulus IIR being better than FIR. We created a function for this purpose. A function that takes the input song, a coefficient that will determine the type of impulse response of the system, and its sampling frequency and returns the fixed song along with the frequency values and where the beep was placed. Figure 16. Response filter graph (r = 0.7)

Now to be able to apply our filter to our signal we create a variable z in which we will obtain the result of the convolution of our filter with the signal x. We use the expression z= conv(x,h), we create another variable Z that takes the absolute values of our function and then to see that it is carried out correctly we suppress the expression sound(Z,fs) verifying that the interference has been eliminated. To finish and visualize the signal after suppression, we plot our variable in absolute values in frequency domain, doing an FFT. In the case of the FIR filter, we obtain the following plot:

Figure 17. Plot of the output and input signal...