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When you pass a signal from two cascaded filters, what happens is that the magnitude response of the whole chain is the product of individual filters, and the phase response is the sum of individual phase responses. This is because the transfer functions are multiplied in the cascade implementation.

So if the frequency response of the single filters are $$H_A(w)=|H_A(w)|e^{j\angle H_A(w)}$$ $$H_B(w)=|H_B(w)|e^{j\angle H_B(w)}$$ then the frequency response of the two cascaded filters (overall) is $$\begin{align} H_{AB}(w)&=H_A(w)H_B(w)\\ &=\left(|H_A(w)|e^{j\angle H_A(w)}\right)\left(|H_B(w)|e^{j\angle H_B(w)}\right)\\ &=|H_A(w)||H_B(w)|e^{j(\angle H_A(w)+\angle H_B(w))} \end{align}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filters. Use abs and angle to find the magnitude and phase.

When you pass a signal from two cascaded filters, what happens is that the magnitude response of the whole chain is the product of individual filters, and the phase response is the sum of individual phase responses. This is because the transfer functions are multiplied in the cascade implementation.

So if the frequency response of the single filters are $$H_A(w)=|H_A(w)|e^{j\angle H_A(w)}$$ $$H_B(w)=|H_B(w)|e^{j\angle H_B(w)}$$ then the frequency response of the two cascaded filters (overall) is $$\begin{align} H_{AB}(w)&=H_A(w)H_B(w)\\ &=\left(|H_A(w)|e^{j\angle H_A(w)}\right)\left(|H_B(w)|e^{j\angle H_B(w)}\right)\\ &=|H_A(w)||H_B(w)|e^{j(\angle H_A(w)+\angle H_B(w))} \end{align}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filters. Use abs and angle to find the magnitude and phase:

... [hA,w] = freqz(bA,aA); [hB,w] = freqz(bB,aB); hAB = hA.*hB; MagResp = 20*log10(abs(hAB)); PhaseResp = angle(hAB); plot(w,MagResp) ... 

when the two filters are identical, then the overall magnitude is squared and the overall phase is scaled by two: $$\begin{align} H_{AA}(w)&=\left(|H_A(w)|e^{j\angle H_A(w)}\right)\left(|H_A(w)|e^{j\angle H_A(w)}\right)\\ &=|H_A(w)|^2e^{j2\angle H_A(w)} \end{align}$$

When you pass a signal from the same filter twice, what happens is that the magnitude response of the whole chain is the square of that of a single filter, and the phase response is scaled by two. This is because the transfer functions are multiplied in the cascade implementation.

So if the frequency response of the single filter is $$H(w)=|H(w)|e^{j\angle H(w)}$$ then the frequency response of the two cascaded filters (overall) is $$\begin{align} H_c(w)&=\left(|H(w)|e^{j\angle H(w)}\right)\left(|H(w)|e^{j\angle H(w)}\right)\\ &=|H(w)|^2e^{j2\angle H(w)} \end{align}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filter. Use abs and angle to find the magnitude and phase.

When you pass a signal from two cascaded filters, what happens is that the magnitude response of the whole chain is the product of individual filters, and the phase response is the sum of individual phase responses. This is because the transfer functions are multiplied in the cascade implementation.

So if the frequency response of the single filters are $$H_A(w)=|H_A(w)|e^{j\angle H_A(w)}$$ $$H_B(w)=|H_B(w)|e^{j\angle H_B(w)}$$ then the frequency response of the two cascaded filters (overall) is $$\begin{align} H_{AB}(w)&=H_A(w)H_B(w)\\ &=\left(|H_A(w)|e^{j\angle H_A(w)}\right)\left(|H_B(w)|e^{j\angle H_B(w)}\right)\\ &=|H_A(w)||H_B(w)|e^{j(\angle H_A(w)+\angle H_B(w))} \end{align}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filters. Use abs and angle to find the magnitude and phase.

When you pass a signal from the same filter twice, what happens is that the magnitude response of the whole chain is the square of that of a single filter, and the phase response is scaled by two.

So if the frequency response of the single filter is $$H(w)=|H(w)|e^{j\angle H(w)}$$ then the frequency response of the two cascaded filters (overall) is $$H_c(w)=|H(w)|^2e^{(j2\angle H(w))}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filter. Use abs and angle to find the magnitude and phase.

When you pass a signal from the same filter twice, what happens is that the magnitude response of the whole chain is the square of that of a single filter, and the phase response is scaled by two. This is because the transfer functions are multiplied in the cascade implementation.

So if the frequency response of the single filter is $$H(w)=|H(w)|e^{j\angle H(w)}$$ then the frequency response of the two cascaded filters (overall) is $$\begin{align} H_c(w)&=\left(|H(w)|e^{j\angle H(w)}\right)\left(|H(w)|e^{j\angle H(w)}\right)\\ &=|H(w)|^2e^{j2\angle H(w)} \end{align}$$

You can use [h,w] = freqz(b,a) in Matlab to get the frequency response of your desired filter. Use abs and angle to find the magnitude and phase.