Types/Methods/Functions

z = LTIreceiverDTI([r],𝐩ᵣ,𝐛,G)
z = LTIreceiverDTI(r,𝐩ᵣ,𝐛,G)

Create an LTI Omnidirectional Receiver by calling LTIreceiverDTI() with a vector of single reflection, r, provided by calling pointReflector(), the receiver position, $\mathsf{p}_\mathrm{r}$ , a time-invariant beam center, $\bm{b}_\mathrm{r}$ and the source antenna's gain, $\mathrm{G}_\mathrm{r}(\Theta)$ relative to beam center $\bm{b}_\mathrm{r}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 𝐛 = [1.0,0.0]
 G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
 q = LTIsourceDTI(𝐩ₛ, p, 𝐛, G)
 α = -0.7; 𝛏 = [3.75e-06c,0.0]
 r = pointReflector(𝛏,α,q)
 z = LTIreceiverDTI([r],𝐩ᵣ,𝐛,G)

In order to observe the multiple reflection, we create an LTI Omnidirectional Receiver by calling LTIreceiverDTI() with the observed multiple reflection, r, provided by calling pointReflector(), the receiver position, $\mathsf{p}_\mathrm{r}$, a time-invariant beam center, $\bm{b}_\mathrm{r}$ and the source antenna's gain, $\mathrm{G}_\mathrm{r}(\Theta)$ relative to beam center $\bm{b}_\mathrm{r}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 𝐛 = [1.0,0.0]
 G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
 q = LTIsourceDTI(𝐩ₛ, p, 𝐛, G)
 α₀ = -0.7; 𝛏₀ = [3.75e-06c,0.0]
 α₁ = -0.7; 𝛏₁ = [1.5e-06c,0.0]
 α₂ = -0.7; 𝛏₂ = [2.5e-06c,0.0]
 r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])
 z = LTIreceiverDTI(r,𝐩ᵣ,𝐛,G)

z = LTIreceiverO([r],𝐩ᵣ)
z = LTIreceiverO(r,𝐩ᵣ)

Create an LTI Omnidirectional Receiver by calling LTIreceiverO() with a vector of single reflection, r, provided by calling pointReflector(), and the receiver position, $\mathsf{p}_\mathrm{r}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTIsourceO(𝐩ₛ, p)
 α = -0.7; 𝛏 = [3.75e-06c,0.0]
 r = pointReflector(𝛏,α,q)
 z = LTIreceiverO([r],𝐩ᵣ)

In order to observe the multiple reflections, we create an LTI Omnidirectional Receiver by calling LTIreceiverO() with the observed multiple reflection, r, provided by calling pointReflector() and the receiver position, $\mathsf{p}_\mathrm{r}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTIsourceO(𝐩ₛ, p)
 α₀ = -0.7; 𝛏₀ = [3.75e-06c,0.0]
 α₁ = -0.7; 𝛏₁ = [1.5e-06c,0.0]
 α₂ = -0.7; 𝛏₂ = [2.5e-06c,0.0]
 r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])
 z = LTIreceiverO(r,𝐩ᵣ)

q = LTIsourceDTI(𝐩ₛ, p)

Create an LTI Directional Source by calling LTIsourceDTI() with the source position, $\mathsf{p}_\mathrm{s}$ ,a transmitted signal, $\mathsf{p}(t)$, time-invariant beam center, $\bm{b}_\mathrm{s}$ and the source antenna's gain, $\mathrm{G}_\mathrm{s}(\Theta)$ relative to beam center $\bm{b}_\mathrm{s}.$

Examples

using LTVsystems
𝐩ₛ =  [0.0, 0.0]
tₚ = 1.0e-06
p(t) = δn(t-tₚ,1.0e-07)
𝐛 = [1.0,0.0]
G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
q = LTIsourceDTI(𝐩ₛ, p, 𝐛, G)

q = LTIsourceO(𝐩ₛ, p)

Create an LTI Omnidirectional Source by calling LTIsourceO() with the source position, $\mathsf{p}_\mathrm{s}$ and the transmisson signal, $\mathsf{p}(t)$.

Examples

using LTVsystems
𝐩ₛ =  [0.0, 0.0]
tₚ = 1.0e-06
p(t) = δn(t-tₚ,1.0e-07)
q = LTIsourceO(𝐩ₛ, p)

z = LTVreceiverO([r],𝐩ᵣ)
z = LTVreceiverO(r,𝐩ᵣ)

Create an LTV Omnidirectional Receiver by calling LTVreceiverO() with a vector of single reflection, r, provided by calling pointReflector(), and a time-varying receiver position, $\mathsf{p}_\mathrm{r}(t)$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTVsourceO(𝐩ₛ, p)
 α = -0.7; 𝛏 = [3.75e-06c,0.0]
 r = pointReflector(𝛏,α,q)
 z = LTVreceiverO([r],𝐩ᵣ)

In order to observe the multiple reflections, we create an LTV Omnidirectional Receiver by calling LTVreceiverO() with the observed multiple reflection, r, provided by calling pointReflector() and a time-varying receiver position, $\mathsf{p}_\mathrm{r}(t)$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTVsourceO(𝐩ₛ, p)
 α₀ = -0.7; 𝛏₀ = [3.75e-06c,0.0]
 α₁ = -0.7; 𝛏₁ = [1.5e-06c,0.0]
 α₂ = -0.7; 𝛏₂ = [2.5e-06c,0.0]
 r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])
 z = LTVreceiverO(r,𝐩ᵣ)

q = LTVsourceO(𝐩ₛ, p)

Create an LTV Omnidirectional Source by calling LTVsourceO() with time-varying source position, $\mathsf{p}_\mathrm{s}(t)$ and the transmisson signal, $\mathsf{p}(t)$.

Examples

using LTVsystems
𝐩ₛ =  [0.0, 0.0]
tₚ = 1.0e-06
p(t) = δn(t-tₚ,1.0e-07)
q = LTVsourceO(𝐩ₛ, p)

z = STATreceiverD([r],𝐩ᵣ,𝐛,G)
z = STATreceiverD(r,𝐩ᵣ,𝐛,G)

Create an LTI Omnidirectional Receiver by calling STATreceiverD() with a vector of single reflection, r, provided by calling pointReflector(), the receiver position, $\mathsf{p}_\mathrm{r}$ , a time-varying (rotating) beam center, $\bm{b}_\mathrm{r}(t)$ and the source antenna's gain, $\mathrm{G}_\mathrm{r}(\Theta)$ relative to beam center $\bm{b}_\mathrm{r}(t)$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 𝐛(t) = [cos(2π*10*t),0.0]/(norm(cos(2π*10*t)))
 G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
 q = STATsourceD(𝐩ₛ, p, 𝐛, G)
 α = -0.7; 𝛏 = [3.75e-06c,0.0]
 r = pointReflector(𝛏,α,q)
 z = STATreceiverD([r],𝐩ᵣ,𝐛,G)

In order to observe the multiple reflections, we create an LTI Omnidirectional Receiver by calling STATreceiverD() with the observed multiple reflection, r, provided by calling pointReflector(), the receiver position, $\mathsf{p}_\mathrm{r}$, a time-varying (rotating) beam center, $\bm{b}_\mathrm{r}(t)$ and the source antenna's gain, $\mathrm{G}_\mathrm{r}(\Theta)$ relative to beam center $\bm{b}_\mathrm{r}(t)$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 𝐛(t) = [cos(2π*10*t),0.0]/(norm(cos(2π*10*t)))
 G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
 q = STATsourceD(𝐩ₛ, p, 𝐛, G)
 α₀ = -0.7; 𝛏₀ = [3.75e-06c,0.0]
 α₁ = -0.7; 𝛏₁ = [1.5e-06c,0.0]
 α₂ = -0.7; 𝛏₂ = [2.5e-06c,0.0]
 r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])
 z = STATreceiverD(r,𝐩ᵣ,𝐛,G)

q = STATsourceD(𝐩ₛ, p)

Create a Stationary Directional Source by calling STATsourceD() with the source position, $\mathsf{p}_\mathrm{s}$ ,a transmitted signal, $\mathsf{p}(t)$, time-varying (rotating) beam center, $\bm{b}_\mathrm{s}(t)$ and the source antenna's gain, $\mathrm{G}_\mathrm{s}(\Theta)$ relative to beam center $\bm{b}_\mathrm{s}(t).$

Examples

using LTVsystems
𝐩ₛ =  [0.0, 0.0]
tₚ = 1.0e-06
p(t) = δn(t-tₚ,1.0e-07)
𝐛(t) = [cos(2π*10*t),0.0]/(norm(cos(2π*10*t)))
G(θ) = 𝒩ᵤ(θ, μ=0.0, σ=π/8)
q = STATsourceD(𝐩ₛ, p, 𝐛, G)

r = pointReflector(𝛏,α,q)
r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])

Create an LTI Omnidirectional Reflection by calling pointReflector() with a single ideal point reflector, $\bm{\xi}$, a reflection coefficient, $\mathsf{\alpha}$ and the source observation, $\mathsf{q}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTIsourceO(𝐩ₛ, p)
 α = -0.7; 𝛏 = [3.75e-06c,0.0]
 r = pointReflector(𝛏,α,q)

In case of multiple ideal point reflector, we create an LTI Omnidirectional Reflection by calling pointReflector() with a vector of multiple ideal point reflector, $\bm{\xi}_0,\bm{\xi}_1\ldots,\bm{\xi}_n$, corresponding reflection coefficients, $\mathsf{\alpha}_0,\mathsf{\alpha}_1,\ldots,\mathsf{\alpha}_n$ and a vector of source observation, $\mathsf{q}$.

Examples

 using LTVsystems
 𝐩ₛ =  [0.0, 0.0]
 𝐩ᵣ =  𝐩ₛ
 tₚ = 1.0e-06
 p(t) = δn(t-tₚ,1.0e-07)
 q = LTIsourceO(𝐩ₛ, p)
 α₀ = -0.7; 𝛏₀ = [3.75e-06c,0.0]
 α₁ = -0.7; 𝛏₁ = [1.5e-06c,0.0]
 α₂ = -0.7; 𝛏₂ = [2.5e-06c,0.0]
 r = pointReflector([𝛏₀,𝛏₁,𝛏₂],[α₀,α₁,α₂],[q])