A spin-torque nano-oscillator (STNO) driven by a ramped bias current can perform spectrum analysis quickly over a wide frequency bandwidth. The STNO spectrum analyzer operates by injection locking to external microwave signals and produces an output DC voltage $V_{rm dc}$ that temporally encodes the input spectrum. We found, via numerical analysis with a macrospin approximation, that an STNO is able to scan a $10~rm GHz$ bandwidth in less than $100~rm ns$ (scanning rate $R$ exceeds $100~rm MHz/ns$). In contrast to conventional quadratic microwave detectors, the output voltage of the STNO analyzer is proportional to the amplitude of the input microwave signal $I_{rm rf}$ with sensitivity $S = dV_{rm dc}/dI_{rm rf} approx 750~rm mV/mA$. The minimum detectable signal of the analyzer depends on the scanning rate $R$ and, at low $R approx 1~rm MHz/ns$, is about $1~rm pW$.