Illustrate the application of Fast Fourier Tyansform (FFT) through the following examples
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Illustrate the application of Fast Fourier Tyansform (FFT) through the following examples
FFT = fast Fourier Transform. 16) Calculate the maximum magnitude error of a 1024 point FFT for sine wave input signal and rectangle window. What is the frequency resolution of the FFT for a sampl...
FFT = fast Fourier Transform.
16) Calculate the maximum magnitude error of a 1024 point FFT for sine wave input signal and rectangle window. What is the frequency resolution of the FFT for a sample rate of 20 kHz. How can this resolution be increased ? (3)
16) Calculate the maximum magnitude error of a 1024 point FFT for sine wave input signal and rectangle window. What is the frequency resolution of the FFT for a sample rate of 20...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
Signal Processing Question #1 Which of the following is NOT using signals? Group of answer choices...
Signal Processing Question #1 Which of the following is NOT using signals? Group of answer choices Morning fog on a pond A traffic light turning red The scent and color of a flower A pump that turns on as water levels rise A call on your cell phone Data collected from a temperature sensor Music from a radio A ship's navigation system Question #2 I would like to have a reliable measurement system, therefore I would like a: Group of...
A voltage signal is created by adding the output from a white noise generator and from...
A voltage signal is created by adding the output from a white noise generator and from a sinewave generator. The white noise is band limited in the range 30 to 80 Hz and has a root mean square value (rms) of 1.5 V. The sine wave has a frequency of 50 Hz and an amplitude of 1.0 V. The signal is digitized at 200 samples per second and a spectral density is obtained by the Fast Fourier Transfer (FFT) algorithm,...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +j2 exp(-j10t) +3 -j2 exp^10t)+ (2-j2) expG300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t) d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part oft(t) by at least 50%. Write down its H(0) and plot its spectrum. e. Plot the spectrum...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t)+j...
Please solve parts d and e
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t)+j2 exp(-j10t) +3 -j2 exp(j10t) + (2-j2) exp(300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t). d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part of f(t) by at least 50%. Write down its H(o) and...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396]...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
can you please solve this problem step by step, thank you!! 1. Consider a DSB-SC signal...
can you please solve this problem step by step, thank
you!!
1. Consider a DSB-SC signal with noise passes through a demodulator shown below. ViC0) 2(0) но но 0) The input signal plus noise is v,(t)-5,() + n'(t) where 5,0): Am(1)cos2r/rt, m(1) cos 2π/J is the message signal with f-</м , carrier frequency is f> fe , and noise n' (r) has power spectral density function G,じ)= η . The local carrier is v,(1)s 2 cosZrw. The carrier filter is...
please select all the right answers QUESTION 1 Analyzer's task is to 0 A. Perform required...
please select all the right answers
QUESTION 1 Analyzer's task is to 0 A. Perform required computation with digital signals. O8. Convert analog time-domain signals into digital frequency domain information. Use digital Fourier transform to perform computation. DConvert digital frequency domain information into analog time-domain signals. QUESTION 2 When performing digital signal analysis O A- Sampling frequency needs to be at least 4 times the slowest frequency of the signal. Aliasing can occur whe n the sampling rate is too...
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...
FFT = fast Fourier Transform.
16) Calculate the maximum magnitude error of a 1024 point FFT for sine wave input signal and rectangle window. What is the frequency resolution of the FFT for a sample rate of 20 kHz. How can this resolution be increased ? (3)
16) Calculate the maximum magnitude error of a 1024 point FFT for sine wave input signal and rectangle window. What is the frequency resolution of the FFT for a sample rate of 20...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +j2 exp(-j10t) +3 -j2 exp^10t)+ (2-j2) expG300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t) d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part oft(t) by at least 50%. Write down its H(0) and plot its spectrum. e. Plot the spectrum...
Please solve parts d and e
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t)+j2 exp(-j10t) +3 -j2 exp(j10t) + (2-j2) exp(300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t). d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part of f(t) by at least 50%. Write down its H(o) and...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
can you please solve this problem step by step, thank
you!!
1. Consider a DSB-SC signal with noise passes through a demodulator shown below. ViC0) 2(0) но но 0) The input signal plus noise is v,(t)-5,() + n'(t) where 5,0): Am(1)cos2r/rt, m(1) cos 2π/J is the message signal with f-</м , carrier frequency is f> fe , and noise n' (r) has power spectral density function G,じ)= η . The local carrier is v,(1)s 2 cosZrw. The carrier filter is...
please select all the right answers
QUESTION 1 Analyzer's task is to 0 A. Perform required computation with digital signals. O8. Convert analog time-domain signals into digital frequency domain information. Use digital Fourier transform to perform computation. DConvert digital frequency domain information into analog time-domain signals. QUESTION 2 When performing digital signal analysis O A- Sampling frequency needs to be at least 4 times the slowest frequency of the signal. Aliasing can occur whe n the sampling rate is too...
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...
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