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3

In general, there is no such requirement for notch filters that $H(e^{j0})=H(e^{j\pi})$ must be satisfied. You could definitely have a notch filter with $H(e^{j0})\neq H(e^{j\pi})$. Having the same gain at DC and at Nyquist is just a practical definition, and if you have a sufficient number of degrees of freedom (i.e., filter coefficients) you might as well ...


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First of all, it's not correct to say "poles should (always) be inside the unit circle for an LTI system to be stable" ; unless it's implied that system is also causal. Otherwise, if the system is noncausal, then its poles should be outside of unit circle for the system being stable. For IIR systems that are described by LCCDEs causality must be externally ...


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Well, you're not going to send and receive those symbols directly, you know? What you'll need to convey the information over a channel is a waveform. Your receiver will then typically use the same waveform to correlate the signal. Say you are using root raised cosine pulses to transmit, then your receiver will employ a root raised cosine filter as a pulse ...


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Fistly, you need to pad the data (y) and the filter (Hamming window). The minimum required length to avoid circular convolution = data length + filter length - 1. In this case, it is 100 + 7 - 1 = 106. For convenient, you may choose power of 2 length, in this case 128. So, pad the data to 128, do fft on it. Pad the filter to 128, do fft on it. Multiply ...


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Based on your exploration of the topics I can make the following explanation, mostly following the approach in Statistical Digital Signal Processing and Modeling, HAYES. Linear Time Invariant (LTI) filtering is associated with the following LCCDE (Linear Constant Coefficient Difference Equation) with zero initial conditions and assuming a causal solution; i....


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A matched filter is matched to a noiseless known waveform. A Weiner Filter is based on the correlation structure of a random waveform. The signal models are different but often a signal has deterministic and random characteristics. It would be a stretch to say that a Kalman Filter could reduce to a matched filter, but it does work in models without ...


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First of all the Wiener filter does not remove the noise but reduce it for WSS signals. It does this based on the relationship between the power spectral density of the clean signal $x[n]$ and imposed noise $v[n]$, both assumed as WSS. The frequency response of a noncausal IIR Wiener filter is given as $$ H(\omega) = \frac{ P_x(\omega) }{ P_x(\omega) + ...


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The notation for discrete-time signals, $x[n]$, was first noticed by me in the original Oppenheim and Schaffer (1975), even though i didn't see that book until 1981. So before, discrete-time signals in DSP used the same notation in mathematics used for sequences (infinite or not), with the subscript, $x_n$. In both notations, the argument or subscript play ...


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Yes, you can bandpass the QPSK signal before matched filtering and demodulation if you wish to do so, but what you need to devote some thought to is whether such an action is a wise decision. The answer might depend on various parameters that you have left unspecified. Bandwidth of bandpass filter $<$ QPSK signal bandwidthIn this case, the filtered QPSK ...


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In image denoising far more important then the noise distribution is the noise spatial correlation properties and the prior about the image. Let's try building some cases and dealing with them. The model is: $ y = x + n $ Where $ x $ is the clan image, $ n $ is the Poisson Noise (With mean $ \lambda $) and $ y $ is the noisy image. Noise Is Poisson ...


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