plz 1. Let and y be the Fourier series coefficients of r(t) and y(t), respectively. Assuming...
3. Let x, and yn be the Fourier series coefficients of (t) and y(t), respectively Assuming the period of r(t) is To. express y, in terms of (a) y(t)-x(at), where a 0. dt 3. Let x, and yn be the Fourier series coefficients of (t) and y(t), respectively Assuming the period of r(t) is To. express y, in terms of (a) y(t)-x(at), where a 0. dt
Let x(t) and y(t) be periodic signals with fundamental period T and Fourier coefficients αn and βn, respectively. Use the properties of Fourier series and find the Fourier series coefficients of the following signals in terms of@n, βn, or both. a) V,(t) = x(t-to) + x(t + to) b) yb (t) = 2x(t-1) + 3y(t-1) c) ye(t) = x(-t) + x(-t-to) d) ya(t)=x(t)y(t) 1.
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
Consider two signals r[n] and y[n] with N = 2 and Fourier series coefficients ao = j, a1 = -2 and , respectively. Compute the periodic convolution d[n] = >_(N) r[r]y[n - r] in two different ways 1, b bo Consider two signals r[n] and y[n] with N = 2 and Fourier series coefficients ao = j, a1 = -2 and , respectively. Compute the periodic convolution d[n] = >_(N) r[r]y[n - r] in two different ways 1, b bo
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal x[n]. i. ii. [5] Use Parseval's relation to determine the average power of x[n]. [5] Let bx be the Fourier series coefficients of a DT signal y[n). Without computing x[n], determine bk in terms of ak if y[n] is related to x[n] by y[n] = ejinx[n] Plot bk for k=0,1,2, ... 7. ak 16
1. (45 pts) DT FS. Find the fundamental period and the Fourier Series (FS) spectral coefficients for these periodic signals. Sketch the spectrum in magnitude and phase. Express each x[n] as the sum of the spectral coefficients for k = [0, N-1]. a. ?1[?] = ???( ? 3 ?) b. ?2 [?] = cos ( ? 3 ?) + sin( ? 4 ?) c. ?3[?]
(a) Let the correlation be defined as r (t) x(T) y (tT) dT T Express R jw= F{r (t)} in terms of X (jw) and Y (jw), the Fourier transform of x (t) and y (t) respectively. (b) Suppose (t) = y (t) = e-H. Find R (jw) using frequency domain properties and the relationship derived in (a) extra Find R (jw) by evaluating the convolution integral in the time domain to get r (t) and then doing the FT.
1. Using the Fourier series analysis Equation 3 for the periodic function r(t) shown in Figure 2.1, determine both the DC coefficient ao and a general expression for the other Fourier series coefficients ak. Do this by hand, not in Matlab. Show all your work in your lab report. You can add these pages as hand-written pages, rather than typing them in to your lab report, if you prefer Hint 1: It will be easiest to integrate this function from...
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]