At the cut off frequency $w_c=\dfrac{w_{s}}{2}$ , magnitude is 0.636. When compared with an ideal low pass filter, we see that instead of cutting of sharply at $w=\frac{w_{s}}{2}$ , the amplitude characteristics of $G_{ho}(jw)$ is zero at $\dfrac{w_{s}}{2}$ and integral multiples of $w_{s}$ .

1.2 First Order Hold

When the 1^st two terms of the power series are used to extrapolate f(t), over the time interval , the device is called a first order hold (FOH). Thus

Impulse response of FOH is obtained by applying a unit impulse at t = 0 , the corresponding output is obtained by setting k = 0,1,2,.....

Since, f(T) = 0 and f(0) = 1, $f_{h1}(t)=1-\dfrac{t}{T}$ in this region. f_h₁(t) is 0 for t > 2T ,

since f(t) = 0 for t ≥ 2T. Figure 4 shows the impulse response of first order hold.