You signed in with another tab or window.Reload to refresh your session.You signed out in another tab or window.Reload to refresh your session.You switched accounts on another tab or window.Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: content/frequency_domain.rst
+5-5Lines changed: 5 additions & 5 deletions
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -119,19 +119,19 @@ Mathematically, the "transform" we use to go from the time domain to the frequen
119
119
..math::
120
120
X(f) =\int x(t) e^{-j2\pi ft} dt
121
121
122
-
For a signal x(t) we can get the frequency domain version, X(f), using this formula. We will represent the time domain version of a function with x(t) or y(t), and the corresponding frequency domain version with X(f) and Y(f). Note the"t" for time, and"f" for frequency. The"j" is simply the imaginary unit. You may have seen it as"i" in high school math class. We use "j" in engineering and computer science because "i" is often referring to current, and in programming it's often used as an iterator.
122
+
For a signal:math:`x(t)` we can get the frequency domain version,:math:`X(f)`, using this formula. We will represent the time domain version of a function with:math:`x(t)` or:math:`y(t)`, and the corresponding frequency domain version with:math:`X(f)` and:math:`Y(f)`. Note the:math:`t` for time, and:math:`f` for frequency. The:math:`j` is simply the imaginary unit, you may have seen it as:math:`i` in high school math class. We use "j" in engineering and computer science because "i" is often referring to current, and in programming it's often used as an iterator.
123
123
124
-
To return to the time domain from frequency is almost the same, aside from ascaling factor andnegative sign:
124
+
To return to the time domain from frequency is almost the same, aside from a negative sign:
125
125
126
126
..math::
127
-
x(t) =\frac{1}{2\pi}\int X(f) e^{j2\pi ft} df
127
+
x(t) =\int X(f) e^{j2\pi ft} df
128
128
129
-
Note that a lot of textbooks and other resources use:math:`w` in place of the:math:`2\pi f`.:math:`w` is angular frequency in radians per second, while:math:`f` is in Hz. All you have to know is that
129
+
Note that a lot of textbooks and other resources use:math:`w` in place of the:math:`2\pi f`, where:math:`w` is angular frequency in radians per second, while:math:`f` is in Hz. All you have to know is that
130
130
131
131
..math::
132
132
\omega =2\pi f
133
133
134
-
Even though it adds a:math:`2\pi` term to many equations, it's easier to stick with frequency in Hz. Ultimately you willwork with Hz inyour SDRapplication.
134
+
Even though it adds a:math:`2\pi` term to many equations, it's easier to stick with frequency in Hz, as wework with Hz inmost SDRand RF signal processing applications.
135
135
136
136
The above equation for the Fourier Transform is the continuous form, which you will only see in math problems. The discrete form is much closer to what is implemented in code: