For many applications, it is useful to have a system that will generate a sinusoidal seq...

For many applications, it is useful to have a system that will generate a sinusoidal sequence. One possible way to do this is with a system whose impulse response is The real and imaginary parts of h[n] are therefore hr [n] = (cos ω₀n)u[n] and hi [n] = (sin ω₀n)u[n], respectively.

In implementing a system with a complex impulse response, the real and imaginary parts are distinguished as separate outputs. By first writing the complex difference equation required to produce the desired impulse response and then separating it into its real and imaginary parts, draw a flow graph that will implement this system. The flow graph that you draw should have only real coefficients. This implementation is sometimes called the coupled form oscillator, since, when the input is excited by an impulse, the outputs are sinusoidal.