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Exercise 3.2Z: Bessel Spectrum
Consider the complex signal For example, the equivalent low-pass signal at the output of an angle modulator (PM, FM) can be represented in this for

8 KB (1,212 words) - 15:51, 9 April 2022
Exercise 1.1Z: Non-redundant Binary Source
[[File:P_ID1257__Dig_Z_1_1.png|right|frame|Dirac-shaped source signal]] ...angle q_\nu \rangle$  in an equivalent way by the Dirac-shaped source signal

4 KB (665 words) - 12:45, 29 April 2022
Exercise 1.3: Rayleigh Fading
* the signal reaches the receiver through many paths, but their transit times are approx ...ass range  $($that is, around the frequency  $f = 0)$,  the signal transmission is described completely by the equation

7 KB (1,034 words) - 15:41, 28 May 2021
Linear and Time Invariant Systems/System Description in Time Domain
...al Representation»  it was explained that for any deterministic signal  $x(t)$  a  »spectral function«  $X(f)$&nbs ...mation about the spectral function is already contained in the time domain representation, even if not always immediately recognizable.  The same facts apply to

14 KB (2,235 words) - 17:21, 2 November 2023
Exercise 2.4Z: Low-pass Influence with Synchronous Demodulation
...gnal  $q(t)$,  the transmitted signal  $s(t)$  and the signal  $b(t)$  in the synchronous demodulator before the low-pass filte ...shows the source signal  $q(t)$  at the top and the transmission signal  $s(t)$  in the middle.

6 KB (938 words) - 16:32, 25 March 2022
Exercise 4.2Z: Multiplication with a Sine Signal
A periodic message signal  $q(t)$  is considered, whose spectral function  $Q(f)$&nbsp ...bsp; $z(t)$, whose spectrum  $Z(f)$  is also shown, leads to the signal  $s(t) = q(t) \cdot z(t).$

5 KB (794 words) - 14:21, 18 January 2023
Exercise 5.4Z: On the Hanning Window
...requently used Hanning window are to be derived.  The continuous-time representation in the interval from  $-T_{\rm P}/2$  to  $+T_{\rm P}/2$&nbs The upper graph shows the discrete-time representation  $w(\nu) = w({\nu} \cdot T_{\rm A})$, where  $T_{\rm A}$  i

7 KB (1,102 words) - 04:18, 18 September 2022
Theory of Stochastic Signals/Probability Density Function (PDF)
...D41__Sto_T_3_1_S1_neu.png |right|frame| Signal and PDF of a Gaussian noise signal]] The graphic shows a section of a stochastic noise signal  $x(t)$  whose instantaneous value can be taken as a continuous r

11 KB (1,672 words) - 10:32, 12 April 2023
Exercise 1.4Z: Representation of Oscillations
...sp; which is shown in the graph together with the corresponding analytical signal  $z_+(t)$.  These signals can be described mathematically as fol Subtask  '''(4)'''  refers to the equivalent low-pass signal  $z_{\rm TP}(t)$,  which is related to  $z_+(t)$  as fo

8 KB (1,330 words) - 18:07, 16 November 2021
Exercise 1.8Z: Cosine-Square Low-Pass Filter
When studying digital systems a dirac-shaped input signal $x(t) = T \cdot \delta(t)$  is often assumed such that  $X(f ...dimensionless in cotrast to the impulse response  $h(t)$ . This signal can also be represented as follows by applying trigonomic transformations:

7 KB (1,063 words) - 19:43, 9 September 2021
Exercise 5.2: Inverse Discrete Fourier Transform
...ients  $d(\nu)$   ⇒   samples of the continuous-time signal  $x(t)$. ...er set describes the discrete form of the Fourier correspondence of the DC signal:

7 KB (1,012 words) - 15:38, 16 May 2021
Signal Representation/Fourier Series
The  »'''Fourier series'''«  of a periodic signal  $x(t)$  is defined as follows: ...e  »'''basic circular frequency'''«  of the periodic signal  $(T_0$ is the period duration$)$.}}

20 KB (3,164 words) - 17:21, 15 November 2023
Exercise 2.2Z: Distortion Power again
...n the graph. This is given by the spectrum of the corresponding analytical signal: ...on|Analytical Signal and its Spectral Function]]  of the book "Signal Representation".

8 KB (1,213 words) - 22:54, 12 September 2021
Theory of Stochastic Signals/Stochastic System Theory
*the structure and representation of  »digital filters«  (non-recursive and recursive), ...operties of the  »Wiener-Kolmogorow filter«  for the signal reconstruction.

17 KB (2,779 words) - 10:17, 22 December 2022
Exercise 2.4: Dual Code and Gray Code
...y transmitted signal,  both derived from the blue drawn binary source signal  $q(t)$.  ...; '''Gray code'''.  This is characterized by the fact that the binary representation of adjacent amplitude values always differ only in a single bit.

6 KB (859 words) - 16:46, 16 May 2022
Period Duration of Periodic Signals
*The maximum value  $x_{\rm max}$  and a signal value  $x(t_*)$  at a given time  $t_*$ are also output. A periodic signal  $x(t)$  is present exactly when it is not constant and if for al

10 KB (1,597 words) - 19:05, 21 March 2023
Physical Signal & Analytic Signal
...the associated analytic signal $x_+(t)$. It is assumed that the band-pass signal $x(t)$ has a frequency-discrete spectrum $X(f)$: The physical signal $x(t)$ is thus composed of three harmonic oscillations, a constellation tha

25 KB (4,242 words) - 14:54, 13 April 2023
Exercise 3.5: Differentiation of a Triangular Pulse
....png|250px|right|frame|Triangular signal and <br>differentiated triangular signal]] We are looking for the spectrum  $Y(f)$  of the signal

6 KB (1,025 words) - 14:19, 24 May 2021
Exercise 4.14: ACF and CCF for Square Wave Signals
We consider a periodic square wave signal  $p(t)$  corresponding to the top sketch with the two possible am Below this is drawn the random signal  $z(t)$:

11 KB (1,709 words) - 17:57, 26 March 2022
Exercise 5.4: Comparison of Rectangular and Hanning Window
Let the time course of a periodic signal be given in principle: ...nbsp; and  $T_{\rm P}$.  The time  $T_{\rm P}$  of the signal section to be analyzed can be set by the user as desired.

8 KB (1,233 words) - 14:24, 18 January 2023