(Fourier Transform -6 points) The Fourier and inverse Fourier transform can be used to transform information between time and frequency domain representations. Figure 1 below illustrates a few examples of this transformation for a few common waveforms, including the corresponding Fourier coefficients. In Fourier analysis a time domain signal can be decomposed into a series of its constituent sinusoidal functions as described by: f(t)=a0+n=1ancos(nw0t)+bnsin(nw0t) where w0 is the angular frequency, i.e. w0=2/T where T is the period of f(t). Using the information in Figure 1, report the first four terms (i.e. for n=0 to n=3 ) of the Fourier decomposition for the time-domain signal presented in Figure 2; i.e., present the series of sine and cosine functions that would reconstruct the original time-domain signal. Figure 1 Time and frequency domain representations of some common waveforms along with the Fourier coefficients based on the functional result of the Fourier transform. "All even barmonics are zero" means that an=0 when n is even. Figure 2 Time domain triangle wave where the y-axis is measured in units of Volts and the x-axis is measured in units of microseconds (Fourier Transform -6 points) The Fourier and inverse Fourier transform can be used to transform information between time and frequency domain representations. Figure 1 below illustrates a few examples of this transformation for a few common waveforms, including the corresponding Fourier coefficients. In Fourier analysis a time domain signal can be decomposed into a series of its constituent sinusoidal functions as described by: f(t)=a0+n=1ancos(nw0t)+bnsin(nw0t) where w0 is the angular frequency, i.e. w0=2/T where T is the period of f(t). Using the information in Figure 1, report the first four terms (i.e. for n=0 to n=3 ) of the Fourier decomposition for the time-domain signal presented in Figure 2; i.e., present the series of sine and cosine functions that would reconstruct the original time-domain signal. Figure 1 Time and frequency domain representations of some common waveforms along with the Fourier coefficients based on the functional result of the Fourier transform. "All even barmonics are zero" means that an=0 when n is even. Figure 2 Time domain triangle wave where the y-axis is measured in units of Volts and the x-axis is measured in units of microseconds