Removing Out Of Band Noise Using Linear Phase Filter - Assignment Example

REMOVING OUT OF BAND NOISE USING LINEAR PHASE FILTER Name Unit Title Institutional Affiliation Date One of the essential components in operation of a majority of electronic circuits is filters. A filter can be described as an electrical network which changes the phase characteristics and or the amplitude of a signal according to frequency. They are prevalently used to emphasize signals within a certain range of frequency and reject some of them in other frequency ranges. With them, it is possible to draw curves of gain versus frequency or phase versus frequency 9Mitra, and Kuo, 2006). All of these curves can be used to depict filter characteristics. Some of the technology that have been adopted over time include a sigma-delta architecture that is more intensive than the analog types. The technique is essential in digitizing an analog signal that is characteristic of low levels of resolution from ADC at an exceptionally high rate of sampling. On the other hand, linear phase filters either obey an even or odd relation of symmetry. When using linear phase filters, there are inherent boundaries on the frequency response and it depends on the relation symmetry and on whether the filter order(n) is either odd or even. In this case a simulation will be used by utilizing an FDA (filter design and analysis) in the matlab toolbox. The signal of interest is a voice signal that has a maximum frequency of 2kiloHertz while the maximum input of voltage is +/- 0.5V. The system comprises of an eight bit DAC and a ADC codec that has a sampling frequency of 20kilohertz. It is necessary for a signal to be loud enough if it is to be heard and comprehended by a receiver. Additionally, it must be loud enough for it to overpower the noise floor. In cases where the signal is not profoundly louder than noise floor, then it is impossible for the receiver to understand it. Mostly, the noise floor is commonly an approximate of -105dBm in 2.4 Ghz. In fact it is hard to locate noise floor in 2.4Ghz environments. A short term intensified noise floor is mostly as a result of interference emanating out of an interferer that is out-of-band. The interference in buildings can be caused by huge electric motors, heavy industrial equipment or nearby cell towers. In the case of the voice signal described, the frequency that will be utilized in the FDA of the matlab tool is 2kHZ,and the line space to be used is(0,1,frequency). The axis will be +0.5 multiplied by size t of random signal as shown below Trial>>rng default; Trial>> Fs=2000; Trial>> t= linspace (0,1,Fs); Trial>>x=cos (2*pi*100*t) +0.5*(size(t)) ; Trial>> plot(rt,x). After plotting the following was obtained: Upon zooming the following is obtained: From speculation, it is necessary to apply a low pass filter by utilizing the PIR 1 to eliminate noise in the original arrangement. In this case, the cut off frequency will be 200 and the filter will be 20. The magnitude response acquired is as follows; Additionally the group delay is 10 since the filter is 20, resulting from the numerator being 2, as shown in the figure below: When performing filter analysis ,the FV tool is accessed within the FDA tool by clicking on the button indicating full view analysis. Since this tool is dynamically related to the FDA tool, alterations in the design of the filter automatically adjust analysis responses. In the case one wants to import current filters for editing and analysis one can choose import mode and select the filter structure, and then enter the sampling frequency as well as the coefficients before clicking import filter. This kind of system provides a comprehensive environment for a commencement to completion type of filter design (Jackson, 2013). Thus the tool can be used to create, quantize, analyze or adjust filters. A low pass filter is used to permit signals below the pass band or cut off frequency and reduces the amplitude of the cutoff frequency which is also known as the stop band. By eliminating some of the frequency, it is possible for the filter to create a smoothing effect. In other words, the filter creates slow changes in the values of the output to make trends more visible and improve the total signal to noise ratio while maintaining minimal degradation of the signal. Their common uses include: eliminating noise, cleaning up signals, designing interpolators and decimators, and data averaging. An ideal low pass filter does not alter the frequency parts of a signal below appointed cutoff frequency. Also it does not accept all parts above the cutoff frequency. However, it is impossible to design an ideal FIR low pass filter because the required specification is infinitely long. The approximations of finite length to the perfect ideal response results to ripples in both the filter's stop band and pass band, and to a nonzero width of transition between the stop band and pass band. Both the transition width and the ripples are not desirable but are deviations that cannot be avoided when an ideal low pass filter is used to approximate the response using a finite impulse response. In this case,, a linear phase filter has been utilized. Its filter coefficient can obey either an odd or even symmetry relation (Smith, 2011). Its group and phase delay are constant and are equal across a frequency band. A linear phase FIR filter that has an order n, has a group delay of n/2 and filtered signal due to delay is held up by n/2 times. It is this property that protects the signal's wave shape in the pass band hence no distortion of phase. From the figure of magnetic response it is evident that ripples and ringing occur in the response, mostly near the edge of the band where there is a huge ring. The effect known as Gibbs effect and does not die even with increase in filter length. It is possible to minimize its magnitude with a non rectangular window. On the other hand, by multiplying a window in the domain of time, it is possible to cause a convolution in the domain of frequency. It can be done by application to the filter, a 51 Hamming window and show the outcome by utilizing an FV tool. It should be noted that to achieve that, the magnitude has to be squared. Utilizing a Hamming window can greatly minimize the ringing, however, this modification is done at the transition width's and optimality's expense. The functions fir2 and firl lay basis on the process of windowing. The functions can take back a inverse Fourier transform in the case of a given filter order and attributes of a perfect wanted filter. Thus, one of the primary disadvantage of FIR filters over the IIR filter is that they need higher filter order than their counter parts to accomplish a certain performance level. Additionally they have greater delay than their counter parts at equal performance. The key purpose of filtering is performance of a signal change that is frequency-dependent. The design specification for the filter can be the removal of noise which is above a particular cutoff frequency. In fact a specification which is more complete can prompt for specification of the pass band ripple amount. Other precise specifications call for a minimum filter order, need an FIR filter or capricious magnitude response. When one is dealing with sampled signals it is essential to normalize the frequencies to match to Nyquist frequency which is always a half of the sampling frequency. It is because the filter design roles that are present in the toolbox of signal processing run within normalized frequencies, hence, do not need the rate of system sampling as an additional input argument. This frequency is normally within the range of 0 ≤ f ≤ 1. In this case the sampling frequency is 20kHZ and the maximum frequency is 2kHz ,thus the normalized frequency will be 2/10 which is 0.2. Due to that a high pass filter can be used to attenuate noise since they operate within low frequencies especially those near zero (Selesnick, 2005). Additionally, it is important to calculate a normalizing factor. The FDA tool is able to graphically show the normalized cut off frequencies of the pass band and stop band as well as the stop band attenuation and pass band ripple. It is important to use sine waves as stimuli in linear phase filters because they are able to pass through without alteration of their frequency or waveform. In fact, they are phase shifted and simply scaled. Hence, if a response of a system has sinusoidal parts that are not part of the input, then it indicates a kind of non linearity and is always referred to as 'distortion' (Shapley, 2009). On the other hand, if a system's response due to a sinusoidal input having an output of a twisted sine wave at similar frequency as the input, then it is likely that it is linear. The impulse response in this case is anti-symmetric. Inputting signals with different sinusoidal signals to the filter produces amplitude that does not match the previous one, hence showing signs of non-linearity. The jumps are predominantly at the points where the there is a change in the amplitude frequency and the phase is not linear with the frequency. Also, the phase does exceed -pi radians. It is not supposed to do that and one of the techniques that can be used to correct that is unwrapping using Q=unwrap(P) in the matlab tool which will correct the phase angles. The linear phase can be described as the condition whereby the filter's phase response is a straight-line frequency function without the phase wrapping at 180 degrees. It results to the delay being identical at all filter frequencies. Usually, the FIR filters are made to be linear-phase and it is deemed to be linear if it has symmetrical coefficient near the centre coefficient. Measuring the output signal by utilizing the correlation coefficient is a good technique for observing for a need for performing an unwrap procedure. This system can work very well with systems that do not have phase shifts occurring between the output and input and it has a demerit of not being strong on phase errors. An instance is when there is a sinusoid input with an unknown phase. In such a case, a 900 shift of phase between the assumed and actual phase will lead to figure of zero for the correlation coefficient. Thus, it is possible to use the cross spectrum's imaginary portion to compute the difference in the phase of the output signal in relation to the initial signal. A signal corruption can be caused by a huge alteration in the signal amplitude when a comparison with the original is made. A signal of low frequency does not really show a great alteration in the overall signal because it represents a small component of the information if a fixed analysis period is taken. Increasing the signal frequency, the alteration created by noise represents a large part of the overall signal and there is higher corruption than with the signal that has a low frequency. Thus, SNR(signal to noise ratio) depends on the signal. Despite the signal power, noise usually has same power across all frequencies and it explains why there can be a higher SNR for low frequencies than for high frequencies. The additive Gaussian noise can be attenuated by using the command line functions; design filt and firl, as well as the filter designer app. The signal to be used in this case is a 20dB sine wave in additive white Gaussian noise. In this process, the random number generator is set to default for the purpose of getting reproducible results as follows rng default Fs=1000; t = (0,1,Fs); x = cos(2*pi*100*t) + 0.5*randn (size (t)); A low pass FIR filter with 150Hz cutoff frequency and an order equal to 20 is utilized. The Kaiser window has a length of one sample bigger than the order of the filter. When designing firl , the frequency specifications are converted to normalized frequencies in the  [0,1] interval. Applying the filter yields a figure shown below: From this case, it can be argued that FIR filters are better than IIR filters in interpolating and decimating systems. It is because, only percentage of the involved calculation actually needed in the implementation of a decimating FIR needs to be performed in a literal sense. FIR do not utilize feedback and it is the sole inputs that are going to be utilized in calculations. Hence for the decimating FIRs, there is no calculation of the other N-1 outputs. Also for the case of interpolating filters there is no need of multiplying the imputed zeroes with their respective coefficients and sum them because one just omits the addition and multiplications linked to the zeroes. Notably, the process of noise attenuation using filters encounters various challenges. One of the challenges is the settling time of filters for multiplexed channels. This occurs when there is one channel at positive full scale while the other one is at negative full scale. Additionally, there is a need for filters that have a truculent roll off for applications with high levels of noise especially the ones that have interference near the Nyquist zone. Another implication is phase delay and harmonic distortion for nonlinearity cases. Hence designers should ensure that they create practical filters which assist in the process of accomplishing the goals of acquiring an accurate system. It is a difficult task and the tradeoffs have to integrate system specifications, effort of design, resources, cost and response time. References Mitra, S.K. and Kuo, Y., 2006. Digital signal processing: a computer-based approach (Vol. 2). New York: McGraw-Hill. Jackson, L.B., 2013. Digital Filters and Signal Processing: With MATLAB® Exercises. Springer Science & Business Media. Smith, S. (2011). Phase Response. [online] Dspguide.com. Available at: http://www.dspguide.com/ch19/4.htm [Accessed 23 Jun. 2017]. Shapley, R., 2009. Linear and nonlinear systems analysis of the visual system: Why does it seem so linear?: A review dedicated to the memory of Henk Spekreijse. Vision research, 49(9), pp.907-921. Selesnick, I., 2005. Linear-Phase FIR Filters. Read More

case of the voice signal described, the frequency that will be utilized in the FDA of the matlab tool is 2kHZ,and the line space to be used is(0,1,frequency). The axis will be +0.5 multiplied by size t of random signal as shown below Trial>>rng default; Trial>> Fs=2000; Trial>> t= linspace (0,1,Fs); Trial>>x=cos (2*pi*100*t) +0.5*(size(t)) ; Trial>> plot(rt,x). After plotting the following was obtained: Upon zooming the following is obtained: From speculation, it is necessary to apply a low pass filter by utilizing the PIR 1 to eliminate noise in the original arrangement.

In this case, the cut off frequency will be 200 and the filter will be 20. The magnitude response acquired is as follows; Additionally the group delay is 10 since the filter is 20, resulting from the numerator being 2, as shown in the figure below: When performing filter analysis ,the FV tool is accessed within the FDA tool by clicking on the button indicating full view analysis. Since this tool is dynamically related to the FDA tool, alterations in the design of the filter automatically adjust analysis responses.

In the case one wants to import current filters for editing and analysis one can choose import mode and select the filter structure, and then enter the sampling frequency as well as the coefficients before clicking import filter. This kind of system provides a comprehensive environment for a commencement to completion type of filter design (Jackson, 2013). Thus the tool can be used to create, quantize, analyze or adjust filters. A low pass filter is used to permit signals below the pass band or cut off frequency and reduces the amplitude of the cutoff frequency which is also known as the stop band.

By eliminating some of the frequency, it is possible for the filter to create a smoothing effect. In other words, the filter creates slow changes in the values of the output to make trends more visible and improve the total signal to noise ratio while maintaining minimal degradation of the signal. Their common uses include: eliminating noise, cleaning up signals, designing interpolators and decimators, and data averaging. An ideal low pass filter does not alter the frequency parts of a signal below appointed cutoff frequency.

Also it does not accept all parts above the cutoff frequency. However, it is impossible to design an ideal FIR low pass filter because the required specification is infinitely long. The approximations of finite length to the perfect ideal response results to ripples in both the filter's stop band and pass band, and to a nonzero width of transition between the stop band and pass band. Both the transition width and the ripples are not desirable but are deviations that cannot be avoided when an ideal low pass filter is used to approximate the response using a finite impulse response.

In this case,, a linear phase filter has been utilized. Its filter coefficient can obey either an odd or even symmetry relation (Smith, 2011). Its group and phase delay are constant and are equal across a frequency band. A linear phase FIR filter that has an order n, has a group delay of n/2 and filtered signal due to delay is held up by n/2 times. It is this property that protects the signal's wave shape in the pass band hence no distortion of phase. From the figure of magnetic response it is evident that ripples and ringing occur in the response, mostly near the edge of the band where there is a huge ring.

The effect known as Gibbs effect and does not die even with increase in filter length. It is possible to minimize its magnitude with a non rectangular window. On the other hand, by multiplying a window in the domain of time, it is possible to cause a convolution in the domain of frequency. It can be done by application to the filter, a 51 Hamming window and show the outcome by utilizing an FV tool. It should be noted that to achieve that, the magnitude has to be squared. Utilizing a Hamming window can greatly minimize the ringing, however, this modification is done at the transition width's and optimality's expense.

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