Consider the circuit of Figure P7.51. Let the op-amp be an LM741 with $\pm 15$ V bias supplies, and suppose $R_F$ is chosen to be $104 \mathrm{k} \Omega$. Assume $v_{\text {in }}$ is a 1 kHz sinusoidal signal with $1-\mathrm{V}$ amplitude.
a. Determine the appropriate value for $R_{\text {in }}$ if the output is to be high whenever $\left|V_{\mathrm{in}}\right| \geq 0.25 \mathrm{~V}$.
b. Sketch the input and output waveforms.