A signal is said to be a periodic signal if the S(t) = S(t+T), where T...
A signal is said to be a periodic signal if the S(t) = S(t+T), where T is the period of the wave. What is the period of a signal in common terms? Re-write the equation for a sinusoidal wave with half the amplitude and twice the frequency of s(t )
Homework Answers
Time period is the minimum
time after which the signal repeats itself.
Let A be amplitude and T be the time period of signal S(t). A
sinusoidal signal is represented as A'sin(wt), where w is the
angular frequency.
Given A'=A/2 and w'=2w. So, the signal is (A/2)sin(2wt).
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A signal is said to be a periodic signal if the S(t) = S(t+T),
where T...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t)...
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this ...
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
In a coherent detection process, a sinusoidally modulated DSB-SC wave, s(t) = c(t)m(t) where the carrier...
In a coherent detection process, a sinusoidally modulated DSB-SC wave, s(t) = c(t)m(t) where the carrier wave is c(t) =Accos(2πfct) and the message signal is m(t) = Amcos(2πfmt), is applied to a product modulator using a locally generated sinusoid of Ac’ amplitude and is out of phase by φ with respect to the sinusoidal carrier used in the modulation. (a) Draw the block diagram of the coherent detection process and label the block diagram with the information provided above accordingly....
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8...
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8 -10 0.2 0.4 0.6 0.8 t (seconds) (i) What is the amplitude of this signal? ii) What is the period of this signal (in seconds)? (iii) What is the frequency of this signal (in Hertz)? (iv) Write an equation for this signal.
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to b...
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0...
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to 0.5 in time domain. Please find out s(t)'s null-to-null bandwidth.
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to...
The Fourier series of a periodic signal s(2) of period T can be expressed as k...
The Fourier series of a periodic signal s(2) of period T can be expressed as k s(x) = cxexp ( 21 - where the coefficients Ck are given by 7/2 CR 1 T -T/2 | $(z) exp (-27 k -27=cdc T (i) Consider s(2) of period T = 6 and amplitude A= 2: 8(z) = 2 * |< T 2 Compute the Fourier coefficients ok. (ii) Use the identities exp(Trik) + exp(-rik) cos(Tk) = 2 sin(Tk) exp(Trik) – exp(-rik) 2i...
Problem 4: A signal x(t) is given mathematically as follows: x(t) = 4.5+ 3.8cos(27 74t -...
Problem 4: A signal x(t) is given mathematically as follows: x(t) = 4.5+ 3.8cos(27 74t - 31/11) - 2 cos(21 296t+1/3) 4.1. Sketch the spectrum of the signal. Is x(t) periodic? If so, what is its fundamental frequency and what are the signal harmonics? Write down the number of each harmonic (0, 1, 2, ... etc) and the frequency of each harmonic. Verify in MATLAB 4.2. A new signal z(t) is created by adding a sinusoidal signal y(t) to x(t)....
Problem 1: A signal f(t) is said to be periodic if for some positive constant To...
Problem 1: A signal f(t) is said to be periodic if for some positive constant To f(t) = f(t+%), for all t. Determine whether or not each of the following continuous-time signals is periodic. If the signal is period eriodic, determine the fundamental a) f(t) = cos2(20t + π35/180) + sin(40t-725/180) + cos( 10t + π/4) cos(20t-n/4) b) f(t) = 10 cos(t + π/4) + c) f(t) = Σ+0000(-1)"u(t-1-4m) 25 sin(V3t - T/2)
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8 -10 0.2 0.4 0.6 0.8 t (seconds) (i) What is the amplitude of this signal? ii) What is the period of this signal (in seconds)? (iii) What is the frequency of this signal (in Hertz)? (iv) Write an equation for this signal.
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to 0.5 in time domain. Please find out s(t)'s null-to-null bandwidth.
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to...
The Fourier series of a periodic signal s(2) of period T can be expressed as k s(x) = cxexp ( 21 - where the coefficients Ck are given by 7/2 CR 1 T -T/2 | $(z) exp (-27 k -27=cdc T (i) Consider s(2) of period T = 6 and amplitude A= 2: 8(z) = 2 * |< T 2 Compute the Fourier coefficients ok. (ii) Use the identities exp(Trik) + exp(-rik) cos(Tk) = 2 sin(Tk) exp(Trik) – exp(-rik) 2i...
Problem 4: A signal x(t) is given mathematically as follows: x(t) = 4.5+ 3.8cos(27 74t - 31/11) - 2 cos(21 296t+1/3) 4.1. Sketch the spectrum of the signal. Is x(t) periodic? If so, what is its fundamental frequency and what are the signal harmonics? Write down the number of each harmonic (0, 1, 2, ... etc) and the frequency of each harmonic. Verify in MATLAB 4.2. A new signal z(t) is created by adding a sinusoidal signal y(t) to x(t)....
Problem 1: A signal f(t) is said to be periodic if for some positive constant To f(t) = f(t+%), for all t. Determine whether or not each of the following continuous-time signals is periodic. If the signal is period eriodic, determine the fundamental a) f(t) = cos2(20t + π35/180) + sin(40t-725/180) + cos( 10t + π/4) cos(20t-n/4) b) f(t) = 10 cos(t + π/4) + c) f(t) = Σ+0000(-1)"u(t-1-4m) 25 sin(V3t - T/2)
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