The discrete-time Fourier transform (DTFT) is the (conventional) Fourier transform of a discrete-time signal. Its output is continous in frequency and periodic. Example: to find the spectrum of the ...

Yes, this is always true if the input to the DFT is real valued. It's called the "conjugate complex symmetry", because $$X_{N-n} = {X_n}^*$$ where $X_n$ is the DFT output and $()^*$ denotes the ...

Acually Matt's answer already gives one view on the problem here: the DFT is implicitly periodic in both time and frequency domain (see this question). From your parameters we can calculate that your ...

The elements building a lumped system are thought of being concentrated at singular points in space. The classical example is an electrical circuit with passive elements like resistor, inductance and ...

Regarding you're general question about how symbol sychronization is done in OFDM systems: One of the most popular and frequently used techniques is the transmission of one or several pilot symbols ...

The common definition of SNR is the power of the wanted signal divided by the noise power. Suppose you have obtained the wanted and the noise signal as arrays, calculation of the SNR in Matlab before ...

Whether the direct convolution or the FFT/IFFT method is faster depends on the length of the impulse response, $N_\mathrm{i}$ and the signal length $N_\mathrm{s}$. With the formulas taken from here I'...

Yes, if eqs. (2) and (3) hold for any "type of signal" (which they do), then (5) must hold. Inserting (4) into (2) we get $$\mathscr{F}\big\{x^*(t)\big\} = X(-f)$$ and using (3) $$X(-f) = X^*(-f) ... View answer 8 votes As for every t_0\in\mathbb{R} and k\in\mathbb{Z}$$ \begin{eqnarray} &x(t_0+4k\pi) &=\cos(t_0+4k\pi)+\sin(t_0/2+2k\pi)\\ & &=\cos(t_0)+\sin(t_0/2)\\ & ...

All implementation aspects aside, the constellation you propose performs worse than QPSK in an additve white gaussian noise (AWGN) channel. I claim this based on simulations that I have run with ...

Intuitively this is true, because averaging a zero mean noise processes approximates its expectation value - which is zero. More rigorously: If the signal $x$ that you want to observe (estimate, ...

The sampling theorem states that $f_\mathrm{S} \geq 2f_\mathrm{max}$, where $f_\mathrm{S}$ and $f_\mathrm{max}$ are the sampling and maximum signal freuqency, respectively. But there's an additional ...

The sinusoid test signal is given by $$s(t) = V_0\cos(2\pi f_0)$$ and its Fourier transform by $$S(f) = \frac{V_0}{2}\big[\delta(f-f_0) + \delta(f+f_0)\big].$$ Inserted in $S_\mathrm{AM-DSB-C}$ it ...

If you'd like to think analog, an OFDM signal can be written as a sum of weighted complex sinusoidals: $$x(t)=\sum_{k=0}^{N-1}X_k \exp{\left( \mathrm j 2\pi\frac{kf_\mathrm{s}}{N}t \tag{1}\right)},$$...

The frequency resolution $f_\Delta$ is $$f_\Delta = \frac{f_\mathrm{s}}{N},$$ where $f_\mathrm{s}$ is the sampling frequency and $N$ is the FFT size. So $$N = \frac{f_\mathrm{s}}{f_\Delta} = \frac{... View answer Accepted answer 5 votes The basic concept of OFDM is to divide a high-bitrate datastream into N low-bitrate datastreams and to multiplex these low-bitrate datastreams in frequency. That is, every datastream is assigned to ... View answer 5 votes The Hermitian symmetry is used to obtain a real-valued time-domain signal. It is a special case of OFDM called discrete multitone (DMT). It exploits a property of the discrete Fourier transform (DFT), ... View answer Accepted answer 5 votes Given a low-pass signal x that is a realization of random variable X with constant spectral density a=N_0/2 in f=-B\ldots B (and zero otherwise) we can calculate the mean power of that signal ... View answer Accepted answer 5 votes The physical definition of frequency is the number of oscillations per second and measured in Hertz (Hz) or more general: 1/(duration of one period of a periodic event in seconds). In your case the ... View answer Accepted answer 4 votes I understand your confusion because the equation is barely understandable from the information given in the book. It becomes more clear from the original paper by Classen and Meyr  from which it ... View answer Accepted answer 4 votes FFT and IFFT are algorithms that implement the (inverse) discrete Fourier transform (DFT). These transforms convert a signal into another representation, namely the frequency domain, and back. This ... View answer 4 votes For calculating the frequency spectrum of an non-uniformly sampled signal I see two options: Interpolate the data in order to obtain evenly spaced samples before taking the FFT as suggested by Hasan. ... View answer Accepted answer 4 votes In order to avoid inter symbol interference (ISI) the baseband transmit signal must meet Nyquist's first criterion. In frequency domain it can be formulated as follows.$$ \omega_\mathrm{N} = \frac{v_\...

First a comment on your noise-generation process. The Matlab function randn() generates Gaussian noise with zero mean and mean power 1. So steps 2 and 3 are obsolete. If you'd like to achieve a given ...

Theoretically it's possible to do a frequency multiplex of two different protocols with one SDR transmitter. However, the practical main limitation is the speed of the digital-to-analog converter (DAC)...

A frequency offset $f_\mathrm{off}$ between the carrier frequency and the local oscillator (at the receiver) results in a linear phase, i.e. the received signal contains a factor \$\mathrm{exp}(j2\pi ...

Differential BPSK As the information is encoded in the phase difference of two consecutive symbols, phase estimation can be omitted in systems where the carrier phase can be assumed to be constant ...

In LTE downlink, users are multiplexed in both time and frequency domain. The concept of ressource blocks (RB) describes a certain frequency band in a certain time slot. Your understanding of the ...