${\overline{𝜀}}_x$	Average energy per tone in DMT systems
$\overline{C}$	Capacity of the discrete-time AWGN channel
$G(f)$	Energy spectral density (ESD)
$M$	Set of quantizer outputs and set of constellation symbols
$P$	Power (Watts), calligraphic distinguishes from probabilities $P$
$\eta$	Spectral efficiency
$𝔼[\mathsf{\text{X}}]$	Expected value of a random variable
$F_s$	Sampling frequency, $F_s=\; 1∕T_s$
$\gamma$	Noise margin
${\gamma }_t$	Target margin
$\widehat{m}(t)$	Decoded symbol, receiver output
$\widehat{P}(e^{j\mathrm{\Omega }})$	Estimated periodogram
${\widehat{R}}_x[k]$	Autocorrelation for a finite-duration signal
${Ŝ}_x(e^{j\mathrm{\Omega }})$	Periodogram
$\mathcal{\text{P}}$	Average power
$\mathrm{\Omega }$	Discrete-time angular frequency in radians
${\overline{E}}_c$	Average energy of a constellation (Joules)
$R_{\mathrm{\text{sym}}}$	$R_{\mathrm{\text{sym}}}=\; 1∕T_{\mathrm{\text{sym}}}$, Which is called the symbol rate
$R_{\mathrm{\text{sym}}}$	Signaling frequency or symbol rate $R_{\mathrm{\text{sym}}}=\; 1∕T_{\mathrm{\text{sym}}}$
$\sigma$	Standard deviation
$T_s$	Sampling interval
$T_{\mathrm{\text{sym}}}$	Symbol interval
$b$	Number of bits per sample
BW	Bandwidth
$C$	Correlation between two random variables $X$ and $Y$
$D$	Signal space or constellation dimension (e. g., $D\; =\; 2$ for QAM)
$c(t)$	Carrier signal, typically a sinusoid $cos(2\pi f_{c}t\; +{\varphi }_c)$
$E_p$	Energy of the shaping pulse
$f_0$	Fundamental frequency (Hz)
$f_c$	Cutoff frequency
$f_p$	Bandpass frequency
$f_r$	Stopband frequency

$H(e^{j\mathrm{\Omega }})$	Frequency response of a discrete-time system
$H(f)$	Frequency response of a continuous-time system
$H(s)$	Transfer function of a continuous-time system
$h(t)$ or $h[n]$	Impulse response of a continuous or discrete-time system
$H(z)$	Transfer function of a discrete-time system
$L$	Oversampling factor, given by $L\; =T_{\mathrm{\text{sym}}}∕T_s$
$L_{\mathrm{\text{CP}}}$	Prefix-cyclic length
$M$	Number of symbols in $M$-ary modulation
$m(t)$	Information source
$m_i$	Symbol of a constellation of M symbols
$MS$	Mean-square
$N$	FFT length, and other uses, e. g., number of samples per frame
$N$	Gaussian (normal) distribution $N(\mu ,{\sigma }^2)$
$\nu$	Noise in continuous $\nu (t)$ and discrete-time $\nu [n]$
$P(\omega )$	Spectrum of a shaping pulse in continuous-time
$p(t)$	Shaping pulse (such as the raised cosine)
$Q$	Quality factor or Q-factor
$r(t)$	Received signal
$R_X(s,t)$	Autocorrelation function
$S(f)$	Continuous-time power spectral density (PSD)
$S(e^{j\mathrm{\Omega }})$	Discrete-time PSD
$s(t)$	Transmitter output, which is the channel input
$S_{ms}[k]$	Mean-square spectrum
$W(e^{j\mathrm{\Omega }})$	Discrete-time Fourier transform of $w[n]$
$w[n]$	Rectangular window
$X(\tau ,f)$	Short-time Fourier transform of $x(t)$
$X(e^{j\mathrm{\Omega }})$	Discrete-time Fourier transform of $x[n]$
$X(f)$	Continuous-time Fourier transform of $x(t)$ with $f$ in Hertz
$X(\omega )$	Continuous-time Fourier transform of $x(t)$ with $\omega$ in rad/s
$X(s)$	Laplace transform of $x(t)$
$x(t)$	Continuous-time signal

$X(z)$	Z transform of $x[n]$
$x[n]$	Discrete-time signal
$x_b[n]$	Binary representation of a signal
$x_i[n]$	Integer-valued signal
$x_q(t)$	Quantized continuous-time signal
$x_q[n]$	Digital signal
$x_s(t)$	Sampled signal
$X_N(e^{j\mathrm{\Omega }})$	DTFT of windowed version of $x[n]$ with $N$ samples
$X_T(f)$	Continuous-time Fourier transform of $x_T(t)$
$x_T(t)$	Truncated version of $x(t)$ with duration $T$