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2

I think your problem might be in this line: FFTSpectrum = fft(sampledsignal,N)'; Note that in MATLAB, ' is the complex conjugate transpose. Use .' to transpose a matrix without applying the complex conjugation.


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In general, one can't infer the magnitude of the DFT coefficients from the values of the input sequence if by inference one means a process that is much more amenable to manual computing than just evaluating the DFT directly. In a sense, you are asking for "half" (or more) of the information that the DFT provides without doing much work for it; TANSTAAFL. ...


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Note that the frequencies of the FFT grid are given by $$f_k=\frac{kf_s}{N},\qquad k=0,1,.\ldots,N-1\tag{1}$$ where $N$ is the FFT length. Now observe that the two frequencies of the given signal fall exactly on the grid. So you only have to determine these two frequencies, and then use $(1)$ to figure out the corresponding indices. EDIT: It's always ...


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Discrete time sequence have frequency $$-\dfrac{1}{2}\leq f\leq \dfrac{1}{2}\tag{1}$$ Continuous time signal $x(t)=A\cdot\sin(2\pi Ft)\tag{2}$ The discrete sequence can be obtained from CT signal through periodic sampling. $$t=n\cdot T= \dfrac{n}{F_s}\tag{3}$$ Plugging the above relation in $(2)$ we get $$f=F/F_s\tag{4}$$ Again plugging the $f$ in $(1)...


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The maximum frequency of a discrete-time signal is half the sampling frequency. A signal with maximum frequency in discrete time is an alternating sequence, and since its period is two sample intervals, its frequency is $f_s/2$. All frequencies in the discrete domain are normalized by that maximum frequency. This implies that a discrete-time system's ...


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The right hand side is the periodic repetition of the left, tells the last equation. Starting from Fourier transform $$X(\omega)=\sum_{n=-\infty}^{\infty}x(n)e^{-j\omega n}$$ and $X(\omega)$ is periodic with period $2\pi$. So only the samples in the fundamental frequency range are sufficient. Now we take $N$ equi-distance samples in the iterval $0\leq\...


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Probably the value of the DCT coefficient and its frequency (i.e., a histogram plot). However, it's impossible to say that with certainty given the information you have provided. If you found that plot in the linked paper, then the definitions of the x- and y-axes are in all likelihood given therein. The paper is behind a paywall, so it's not helpful to ...


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Let's give it a shot. We know that during sampling, we obtained a discretized version, $x(nT_s)$ of a continuous time signal $x(t)$ sampled every $T_s$ seconds. I will denote their corresponding Fourier Transforms as $X_{DT}(e^{j\omega})$ and $X_{CT}(j\Omega)$, respectively, according to the majority of the bibliography. Indices denote discrete time (DT) ...


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