Start with a simple baseband tone Take m ( t ) = cos ⁡ ( ω m t ) m(t)=\cos(\omega_m t) and carrier cos ⁡ ( ω c t ) . \cos(\omega_c t). If we simply multiply them: s ( t ) = m ( t ) cos ⁡ ( ω c t ) s(t)=m(t)\cos(\omega_ct) then s ( t ) = cos ⁡ ( ω m t ) cos ⁡ ( ω c t ) . s(t)=\cos(\omega_mt)\cos(\omega_ct). Using cos ⁡ A cos ⁡ B = 1 2 [ cos ⁡ ( A + B ) + cos ⁡ ( A − B ) ] , \cos A\cos B =\frac12[\cos(A+B)+\cos(A-B)], we get s ( t ) = 1 2 cos ⁡ ( ( ω c + ω m ) t ) + 1 2 cos ⁡ ( ( ω c − ω m ) t ) \boxed{s(t)=\frac12\cos((\omega_c+\omega_m)t)+\frac12\cos((\omega_c-\omega_m)t)} So we get two frequencies : ω c + ω m \boxed{\omega_c+\omega_m} and ω c − ω m . \boxed{\omega_c-\omega_m}. These are the upper sideband (USB) and lower sideband (LSB) . We want only one Suppose we want the upper side...

  MATLAB Code clear; close all; clc; %% Parameters Fs = 1000;          % Sampling frequency T  = 2;             % Duration t  = 0:1/Fs:T-1/Fs; fm = 5;             % Message frequency fc = 100;            % Carrier frequency %% Baseband signal m = cos(2*pi*fm*t); %% Hilbert transform mh = imag(hilbert(m)); %% Analytic signal ma = m + 1j*mh; %% Envelope and instantaneous phase envelope = abs(ma); phase = unwrap(angle(ma)); %% I/Q modulation I = m; Q = mh; USB = I .* cos(2*pi*fc*t) ...     - Q .* sin(2*pi*fc*t); LSB = I .* cos(2*pi*fc*t) ...     + Q .* sin(2*pi*fc*t); %% Ordinary DSB-SC DSB = m .* cos(2*pi*fc*t); %% Plot everything figure('Color','w'); subplot(4,2,1) plot(t,m,'b') grid on title('Baseband m(t)') xlabel('Time (s)') subplot(4,2,2) plot(t,mh,'r') grid on title('Hilbert transform m̂(t)') xlabel('Time (s)') subplot(4,2,3)...

  Hilbert Transform & I/Q Simulator Hilbert Transform / Analytic Signal / I-Q Simulator Message frequency Carrier frequency Sampling frequency Duration Run simulation 1. Hilbert Transform m(t) = cos(2π fₘ t) m̂(t) = Hilbert{m(t)} 2. Analytic Signal mₐ(t) = m(t) + j m̂(t) Envelope = |mₐ(t)| 3. I/Q Modulation s(t) = I(t)cos(ωₙt) − Q(t)sin(ωₙt) I(t) = m(t) Q(t) = m̂(t) 4. SSB USB = m(t)cos(ωₙt) − m̂(t)sin(ωₙt) LSB = m(t)cos(ωₙt) + m̂(t)sin(ωₙt) 5. Frequency Domain Return to Premium Virtual DSP Lab →

The Hilbert transform of a signal x ( t ) is x ^ ( t ) = H { x ( t ) } = 1 π PV ∫ − ∞ ∞ x ( τ ) t − τ d τ \boxed{\hat{x}(t)=\mathcal H\{x(t)\} =\frac{1}{\pi}\operatorname{PV}\int_{-\infty}^{\infty} \frac{x(\tau)}{t-\tau}\,d\tau} where PV means the Cauchy principal value , because the kernel 1 t − τ is singular at τ = t . Convolving a time-domain signal f ( t ) f(t) with the Hilbert transform kernel 1 π t \frac{1}{\pi t} pro...

  It is a stack (LIFO) problem. Initial values: R 1 = 25 H , R 2 = 30 H , R 3 = 40 H R_1=25H,\quad R_2=30H,\quad R_3=40H Step 1: PUSH operations We push in this order: P U S H { R 1 } PUSH\{R_1\} Stack: [ 25 H ] [25H] Then: P U S H { R 2 } PUSH\{R_2\} Stack: [ 25 H ,   30 H ] [25H,\ 30H] Then: P U S H { R 3 } PUSH\{R_3\} Stack: [ 25 H ,   30 H ,   40 H ] [25H,\ 30H,\ 40H] The last value pushed is the first value popped . Step 2: POP operations P O P { R 1 } POP\{R_1\} gets the top value: R 1 = 40 H R_1=40H Then: P O P { R 2 } POP\{R_2\} gets: R 2 = 30 H R_2=30H Then: P O P { R 3 } POP\{R_3\} gets: R 3 = 25 H R_3=25H Therefore, R 1 = 40 H , R 2 = 30 H , R 3 = 25 H \boxed{R_1=40H,\quad R_2=30H,\quad R_3=25H} Answer: (a)

  MOSFET Substrate Doping Concentration Solution MOSFET Substrate Doping Concentration Given Gate oxide thickness: \[ t_{ox} = 10\,\text{nm} = 10^{-8}\,\text{m} \] Substrate sensitivity: \[ \frac{\partial V_T}{\partial |V_{BS}|} = 50\,\text{mV/V} = 0.05 \] Substrate voltage: \[ |V_{BS}| = 2\,\text{V} \] Electron charge: \[ q = 1.6\times10^{-19}\,\text{C} \] Vacuum permittivity: \[ \epsilon_0 = 8.85\times10^{-12}\,\text{F/m} \] Relative permittivities: \[ \epsilon_{Si}=12,\qquad \epsilon_{ox}=4 \] ...

GMSK Signal Analyzer Bit Rate (bps) 50 Hz Carrier Frequency (Hz) 500 Hz Space Frequency (Hz) 1 Time-Bandwidth Product (BT) 1 Upload CSV, .wav, .mp3, or .mp4 Use Test Signal CSV Sample Rate (Hz): No Operation FFT (Spectrum) Amplitude Modulation (AM) Double Sideband Supressed Carrier (DSBSC) Pulse Amplitude Modulation (PAM) Flat Top...

MSK Signal Analyzer Bit Rate (bps) 50 Hz Carrier Frequency (Hz) 500 Hz Space Frequency (Hz) 1 Carrier Signal Amplitude (Ac) 1 Upload CSV, .wav, .mp3, or .mp4 Use Test Signal CSV Sample Rate (Hz): No Operation FFT (Spectrum) Amplitude Modulation (AM) Double Sideband Supressed Carrier (DSBSC) Pulse Amplitude Modulation (PAM) Flat To...