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- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/05%3A_Digital_Signal_Processing
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/07%3A_Appendix/7.01%3A_DecibelsFor example, to find the decibel value for \[\sqrt{2} \nonumber \] we halve the decibel value for 2; 26 dB equals 10+10+6 dB that corresponds to a ratio of 10×10×4=400. Because the transfer function m...For example, to find the decibel value for \[\sqrt{2} \nonumber \] we halve the decibel value for 2; 26 dB equals 10+10+6 dB that corresponds to a ratio of 10×10×4=400. Because the transfer function multiplies the input signal's spectrum, to find the output amplitude at a given frequency we simply add the filter's gain in decibels (relative to a reference of one) to the input amplitude at that frequency.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/04%3A_Frequency_Domain/4.09%3A_Linear_Time_Invariant_SystemsWhen we apply a periodic input to a linear, time-invariant system, the output is periodic and has Fourier series coefficients equal to the product of the system's frequency response and the input's Fo...When we apply a periodic input to a linear, time-invariant system, the output is periodic and has Fourier series coefficients equal to the product of the system's frequency response and the input's Fourier coefficients (Filtering Periodic Signals). The middle term in the expression for Y(f) consists of the difference of two terms: the constant 1 and the complex exponential \[e^{-(i2\pi f\Delta )} \nonumber \]
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/03%3A_Analog_Signal_Processing/3.15%3A_Formal_Circuit_Methods_-_Node_MethodIn the above circuit we cannot use the series/parallel combination rules: The vertical resistor at node 1 keeps the two horizontal 1 Ω resistors from being in series, and the 2 Ω resistor prevents the...In the above circuit we cannot use the series/parallel combination rules: The vertical resistor at node 1 keeps the two horizontal 1 Ω resistors from being in series, and the 2 Ω resistor prevents the two 1 Ω resistors at node 2 from being in series. As shown in Figure 3.15.5 below, adding the second resistor has two effects: it lowers the gain in the passband (the range of frequencies for which the filter has little effect on the input) and increases the cutoff frequency.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/05%3A_Digital_Signal_Processing/5.16%3A_Discrete_-Time_Filtering_of_Analog_SignalsThe complexities of time-domain and frequency-domain implementations depend on different aspects of the filtering: The time-domain implementation depends on the combined orders of the filter while the...The complexities of time-domain and frequency-domain implementations depend on different aspects of the filtering: The time-domain implementation depends on the combined orders of the filter while the frequency-domain implementation depends on the logarithm of the Fourier transform's length.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/06%3A_Information_Communication/6.17%3A_Digital_Communication_in_the_Presence_of_NoiseProbability Distribution of the Noise Term — The value of the noise terms relative to the signal terms and the probability of their occurrence directly affect the likelihood that a receiver error will...Probability Distribution of the Noise Term — The value of the noise terms relative to the signal terms and the probability of their occurrence directly affect the likelihood that a receiver error will occur. The term A 2 T equals the energy expended by the transmitter in sending the bit; we label this term E b . We arrive at a concise expression for the probability the matched filter receiver makes a bit-reception error.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/05%3A_Digital_Signal_Processing/5.11%3A_Discrete-Time_SystemsWhen we developed analog systems, interconnecting the circuit elements provided a natural starting place for constructing useful devices. In discrete-time signal processing, we are not limited by hard...When we developed analog systems, interconnecting the circuit elements provided a natural starting place for constructing useful devices. In discrete-time signal processing, we are not limited by hardware considerations but by what can be constructed in software.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/06%3A_Information_Communication
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/00%3A_Front_Matter
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/05%3A_Digital_Signal_Processing/5.12%3A_Discrete-Time_Systems_in_the_Time-DomainThe reason lies in the definition of a linear system: The only way that the output to a sum of signals can be the sum of the individual outputs occurs when the initial conditions in each case are zero...The reason lies in the definition of a linear system: The only way that the output to a sum of signals can be the sum of the individual outputs occurs when the initial conditions in each case are zero. The reason for this terminology is that the unit sample also known as the impulse (especially in analog situations), and the system's response to the "impulse" lasts forever.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/Electrical_Engineering_(Johnson)/06%3A_Information_Communication/6.08%3A_Noise_and_InterferenceAll channels are subject to noise, and we need a way of describing such signals despite the fact we can't write a formula for the noise signal like we can for interference. At each frequency, the phas...All channels are subject to noise, and we need a way of describing such signals despite the fact we can't write a formula for the noise signal like we can for interference. At each frequency, the phase of the noise spectrum is totally uncertain: It can be any value in between 0 and 2π, and its value at any frequency is unrelated to the phase at any other frequency.
