A digital filter is characterized by the following recursive relation, where x(n) and y(n)
A digital filter is characterized by the following recursive relation, where x(n) and y(n) are the input and output samples at the nth sampling instant. The sampling frequency is 100 Hz.
y(n) = 0.8 y(n-1) – 0.64 y(n-2) + x(n) – x(n-1) + x(n-2)
Find the poles and zeros of the discrete time transfer function of the filter. Hencededuce and sketch the magnitude response characteristic of the filter from f =0 to f = infinity. Mark the values at f =0, 50 and 100 Hz.
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A digital filter is characterized by the following recursive relation, where x(n) and y(n)
Digital processing signals For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2)...
Digital processing signals
For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2) a) Draw its block diagram b) b.1 - Obtain its transfer function H(z) b.2-Calculate and PLOT | H(e*)l, for θ 0, π/4. π/2. 3π/4, and π. Obtain and plot its poles and zeros, in the z-plane c)
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t)...
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t) at 6 kHz. The digital is filter described by y(n) -x(n) + 0.8y(n -1) Find an expression for the steady state output if x(t) -3sin(2mft) with f 200 Hz? Hint: evaluate the filter's frequency response at the discrete time frequency corresponding to 200 Hz. (12 points) Anti-alias filter Sample A/D Digital Filter
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
Question 3 Consider a discrete-time signal sequence given as follow: *(n) = cos ) for 0...
Question 3 Consider a discrete-time signal sequence given as follow: *(n) = cos ) for 0 Sns3 3 ) Calculate the 4-point Discrete Fourier Transform (DFT) of x(n). (15 marks) Calculate the radix-2 Fast Fourier Transform (FFT) for x(n). (10 marks) [Total: 25 marks) Ouestion 4 digital low-pass filter design based on an analog Chevyshev Type 1 filter requires to meet the following specifications: Passband ripple: <1dB Passband edge: 500 Hz. Stopband attenuation: > 40 dB Stopband edge: 1000 Hz...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at a sampling rate fs = 180 Hz. Sketch the spectrum X (f) of the sampled signal x (t). Properly label x-axis and y-axis. 2) Now suppose we will use an ideal lowpass filter of gain 1/fs with a cutoff frequency 90 Hz for the sampled signal xs(t). What is the output of the filter x,(t)? 3) Now let's take samples of x(t) at sampling...
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n]...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a)...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
2. The following causal system is excited by white noise (x[n)=w(n)) of zero mean and unit...
2. The following causal system is excited by white noise (x[n)=w(n)) of zero mean and unit variance. The output is y(n). q(n)-x(n) 0.8 q(n-1) y(n) 0.2 q(n) a) Determine the autocorrelation of the output y(n) in closed form for all m. Give numerical values for ry(0), ryy(1), ryy(2) b) Find the variance of y(n). Give a numerical value and show all your work. c) Find the poles and zeros of the power spectral density (PSD) of y(n) and sketch them...
7. Consider the digital filter given by: x[n] yni - 1 2 1 + -1 For...
7. Consider the digital filter given by: x[n] yni - 1 2 1 + -1 For this filter A. Determine if it is an IIR or FIR B. Calculate the difference equation C. Calculate the first four (4) samples of the impulse response D. Calculate the gain at DC (i.e., w = 0) E. Calculate the gain at the Nyquist frequency (i.e., w = 2
Digital processing signals
For SYSTEM 4", characterized by: y(n) x(n) - x(n-2) + 0.2 y(n-1)-0.04 y(n-2) a) Draw its block diagram b) b.1 - Obtain its transfer function H(z) b.2-Calculate and PLOT | H(e*)l, for θ 0, π/4. π/2. 3π/4, and π. Obtain and plot its poles and zeros, in the z-plane c)
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t) at 6 kHz. The digital is filter described by y(n) -x(n) + 0.8y(n -1) Find an expression for the steady state output if x(t) -3sin(2mft) with f 200 Hz? Hint: evaluate the filter's frequency response at the discrete time frequency corresponding to 200 Hz. (12 points) Anti-alias filter Sample A/D Digital Filter
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
Question 3 Consider a discrete-time signal sequence given as follow: *(n) = cos ) for 0 Sns3 3 ) Calculate the 4-point Discrete Fourier Transform (DFT) of x(n). (15 marks) Calculate the radix-2 Fast Fourier Transform (FFT) for x(n). (10 marks) [Total: 25 marks) Ouestion 4 digital low-pass filter design based on an analog Chevyshev Type 1 filter requires to meet the following specifications: Passband ripple: <1dB Passband edge: 500 Hz. Stopband attenuation: > 40 dB Stopband edge: 1000 Hz...
3. (50 points] Consider the signal (t= cos(27 (100)+]: 1) Let's take samples of x(t) at a sampling rate fs = 180 Hz. Sketch the spectrum X (f) of the sampled signal x (t). Properly label x-axis and y-axis. 2) Now suppose we will use an ideal lowpass filter of gain 1/fs with a cutoff frequency 90 Hz for the sampled signal xs(t). What is the output of the filter x,(t)? 3) Now let's take samples of x(t) at sampling...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
2. The following causal system is excited by white noise (x[n)=w(n)) of zero mean and unit variance. The output is y(n). q(n)-x(n) 0.8 q(n-1) y(n) 0.2 q(n) a) Determine the autocorrelation of the output y(n) in closed form for all m. Give numerical values for ry(0), ryy(1), ryy(2) b) Find the variance of y(n). Give a numerical value and show all your work. c) Find the poles and zeros of the power spectral density (PSD) of y(n) and sketch them...
7. Consider the digital filter given by: x[n] yni - 1 2 1 + -1 For this filter A. Determine if it is an IIR or FIR B. Calculate the difference equation C. Calculate the first four (4) samples of the impulse response D. Calculate the gain at DC (i.e., w = 0) E. Calculate the gain at the Nyquist frequency (i.e., w = 2
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