.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "tutorials/audio_resampling_tutorial.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_tutorials_audio_resampling_tutorial.py: Audio Resampling ================ **Author**: `Caroline Chen `__, `Moto Hira `__ This tutorial shows how to use torchaudio's resampling API. .. GENERATED FROM PYTHON SOURCE LINES 10-19 .. code-block:: default import torch import torchaudio import torchaudio.functional as F import torchaudio.transforms as T print(torch.__version__) print(torchaudio.__version__) .. rst-class:: sphx-glr-script-out .. code-block:: none 1.13.0 0.13.0 .. GENERATED FROM PYTHON SOURCE LINES 20-25 Preparation ----------- First, we import the modules and define the helper functions. .. GENERATED FROM PYTHON SOURCE LINES 25-111 .. code-block:: default import math import timeit import librosa import resampy import matplotlib.pyplot as plt import matplotlib.colors as mcolors import pandas as pd from IPython.display import Audio, display pd.set_option('display.max_rows', None) pd.set_option('display.max_columns', None) DEFAULT_OFFSET = 201 def _get_log_freq(sample_rate, max_sweep_rate, offset): """Get freqs evenly spaced out in log-scale, between [0, max_sweep_rate // 2] offset is used to avoid negative infinity `log(offset + x)`. """ start, stop = math.log(offset), math.log(offset + max_sweep_rate // 2) return torch.exp(torch.linspace(start, stop, sample_rate, dtype=torch.double)) - offset def _get_inverse_log_freq(freq, sample_rate, offset): """Find the time where the given frequency is given by _get_log_freq""" half = sample_rate // 2 return sample_rate * (math.log(1 + freq / offset) / math.log(1 + half / offset)) def _get_freq_ticks(sample_rate, offset, f_max): # Given the original sample rate used for generating the sweep, # find the x-axis value where the log-scale major frequency values fall in times, freq = [], [] for exp in range(2, 5): for v in range(1, 10): f = v * 10**exp if f < sample_rate // 2: t = _get_inverse_log_freq(f, sample_rate, offset) / sample_rate times.append(t) freq.append(f) t_max = _get_inverse_log_freq(f_max, sample_rate, offset) / sample_rate times.append(t_max) freq.append(f_max) return times, freq def get_sine_sweep(sample_rate, offset=DEFAULT_OFFSET): max_sweep_rate = sample_rate freq = _get_log_freq(sample_rate, max_sweep_rate, offset) delta = 2 * math.pi * freq / sample_rate cummulative = torch.cumsum(delta, dim=0) signal = torch.sin(cummulative).unsqueeze(dim=0) return signal def plot_sweep( waveform, sample_rate, title, max_sweep_rate=48000, offset=DEFAULT_OFFSET, ): x_ticks = [100, 500, 1000, 5000, 10000, 20000, max_sweep_rate // 2] y_ticks = [1000, 5000, 10000, 20000, sample_rate // 2] time, freq = _get_freq_ticks(max_sweep_rate, offset, sample_rate // 2) freq_x = [f if f in x_ticks and f <= max_sweep_rate // 2 else None for f in freq] freq_y = [f for f in freq if f in y_ticks and 1000 <= f <= sample_rate // 2] figure, axis = plt.subplots(1, 1) _, _, _, cax = axis.specgram(waveform[0].numpy(), Fs=sample_rate) plt.xticks(time, freq_x) plt.yticks(freq_y, freq_y) axis.set_xlabel("Original Signal Frequency (Hz, log scale)") axis.set_ylabel("Waveform Frequency (Hz)") axis.xaxis.grid(True, alpha=0.67) axis.yaxis.grid(True, alpha=0.67) figure.suptitle(f"{title} (sample rate: {sample_rate} Hz)") plt.colorbar(cax) plt.show(block=True) .. GENERATED FROM PYTHON SOURCE LINES 112-148 Resampling Overview ------------------- To resample an audio waveform from one freqeuncy to another, you can use :py:class:`torchaudio.transforms.Resample` or :py:func:`torchaudio.functional.resample`. ``transforms.Resample`` precomputes and caches the kernel used for resampling, while ``functional.resample`` computes it on the fly, so using ``torchaudio.transforms.Resample`` will result in a speedup when resampling multiple waveforms using the same parameters (see Benchmarking section). Both resampling methods use `bandlimited sinc interpolation `__ to compute signal values at arbitrary time steps. The implementation involves convolution, so we can take advantage of GPU / multithreading for performance improvements. .. note:: When using resampling in multiple subprocesses, such as data loading with multiple worker processes, your application might create more threads than your system can handle efficiently. Setting ``torch.set_num_threads(1)`` might help in this case. Because a finite number of samples can only represent a finite number of frequencies, resampling does not produce perfect results, and a variety of parameters can be used to control for its quality and computational speed. We demonstrate these properties through resampling a logarithmic sine sweep, which is a sine wave that increases exponentially in frequency over time. The spectrograms below show the frequency representation of the signal, where the x-axis corresponds to the frequency of the original waveform (in log scale), y-axis the frequency of the plotted waveform, and color intensity the amplitude. .. GENERATED FROM PYTHON SOURCE LINES 148-155 .. code-block:: default sample_rate = 48000 waveform = get_sine_sweep(sample_rate) plot_sweep(waveform, sample_rate, title="Original Waveform") Audio(waveform.numpy()[0], rate=sample_rate) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_001.png :alt: Original Waveform (sample rate: 48000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_001.png :class: sphx-glr-single-img .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 156-163 Now we resample (downsample) it. We see that in the spectrogram of the resampled waveform, there is an artifact, which was not present in the original waveform. This effect is called aliasing. `This page `__ has an explanation of how it happens, and why it looks like a reflection. .. GENERATED FROM PYTHON SOURCE LINES 164-172 .. code-block:: default resample_rate = 32000 resampler = T.Resample(sample_rate, resample_rate, dtype=waveform.dtype) resampled_waveform = resampler(waveform) plot_sweep(resampled_waveform, resample_rate, title="Resampled Waveform") Audio(resampled_waveform.numpy()[0], rate=resample_rate) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_002.png :alt: Resampled Waveform (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_002.png :class: sphx-glr-single-img .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 173-187 Controling resampling quality with parameters --------------------------------------------- Lowpass filter width ~~~~~~~~~~~~~~~~~~~~ Because the filter used for interpolation extends infinitely, the ``lowpass_filter_width`` parameter is used to control for the width of the filter to use to window the interpolation. It is also referred to as the number of zero crossings, since the interpolation passes through zero at every time unit. Using a larger ``lowpass_filter_width`` provides a sharper, more precise filter, but is more computationally expensive. .. GENERATED FROM PYTHON SOURCE LINES 187-194 .. code-block:: default sample_rate = 48000 resample_rate = 32000 resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=6) plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=6") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_003.png :alt: lowpass_filter_width=6 (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 196-200 .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, lowpass_filter_width=128) plot_sweep(resampled_waveform, resample_rate, title="lowpass_filter_width=128") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_004.png :alt: lowpass_filter_width=128 (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 201-212 Rolloff ~~~~~~~ The ``rolloff`` parameter is represented as a fraction of the Nyquist frequency, which is the maximal frequency representable by a given finite sample rate. ``rolloff`` determines the lowpass filter cutoff and controls the degree of aliasing, which takes place when frequencies higher than the Nyquist are mapped to lower frequencies. A lower rolloff will therefore reduce the amount of aliasing, but it will also reduce some of the higher frequencies. .. GENERATED FROM PYTHON SOURCE LINES 212-220 .. code-block:: default sample_rate = 48000 resample_rate = 32000 resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.99) plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.99") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_005.png :alt: rolloff=0.99 (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 222-227 .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, rolloff=0.8) plot_sweep(resampled_waveform, resample_rate, title="rolloff=0.8") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_006.png :alt: rolloff=0.8 (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_006.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 228-238 Window function ~~~~~~~~~~~~~~~ By default, ``torchaudio``’s resample uses the Hann window filter, which is a weighted cosine function. It additionally supports the Kaiser window, which is a near optimal window function that contains an additional ``beta`` parameter that allows for the design of the smoothness of the filter and width of impulse. This can be controlled using the ``resampling_method`` parameter. .. GENERATED FROM PYTHON SOURCE LINES 238-246 .. code-block:: default sample_rate = 48000 resample_rate = 32000 resampled_waveform = F.resample(waveform, sample_rate, resample_rate, resampling_method="sinc_interpolation") plot_sweep(resampled_waveform, resample_rate, title="Hann Window Default") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_007.png :alt: Hann Window Default (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_007.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 248-253 .. code-block:: default resampled_waveform = F.resample(waveform, sample_rate, resample_rate, resampling_method="kaiser_window") plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Default") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_008.png :alt: Kaiser Window Default (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_008.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 254-260 Comparison against librosa -------------------------- ``torchaudio``’s resample function can be used to produce results similar to that of librosa (resampy)’s kaiser window resampling, with some noise .. GENERATED FROM PYTHON SOURCE LINES 260-264 .. code-block:: default sample_rate = 48000 resample_rate = 32000 .. GENERATED FROM PYTHON SOURCE LINES 265-268 kaiser_best ~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 268-279 .. code-block:: default resampled_waveform = F.resample( waveform, sample_rate, resample_rate, lowpass_filter_width=64, rolloff=0.9475937167399596, resampling_method="kaiser_window", beta=14.769656459379492, ) plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Best (torchaudio)") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_009.png :alt: Kaiser Window Best (torchaudio) (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_009.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 281-287 .. code-block:: default librosa_resampled_waveform = torch.from_numpy( librosa.resample(waveform.squeeze().numpy(), orig_sr=sample_rate, target_sr=resample_rate, res_type="kaiser_best") ).unsqueeze(0) plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Best (librosa)") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_010.png :alt: Kaiser Window Best (librosa) (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_010.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 289-293 .. code-block:: default mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item() print("torchaudio and librosa kaiser best MSE:", mse) .. rst-class:: sphx-glr-script-out .. code-block:: none torchaudio and librosa kaiser best MSE: 2.0806901153659937e-06 .. GENERATED FROM PYTHON SOURCE LINES 294-297 kaiser_fast ~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 297-308 .. code-block:: default resampled_waveform = F.resample( waveform, sample_rate, resample_rate, lowpass_filter_width=16, rolloff=0.85, resampling_method="kaiser_window", beta=8.555504641634386, ) plot_sweep(resampled_waveform, resample_rate, title="Kaiser Window Fast (torchaudio)") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_011.png :alt: Kaiser Window Fast (torchaudio) (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_011.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 310-316 .. code-block:: default librosa_resampled_waveform = torch.from_numpy( librosa.resample(waveform.squeeze().numpy(), orig_sr=sample_rate, target_sr=resample_rate, res_type="kaiser_fast") ).unsqueeze(0) plot_sweep(librosa_resampled_waveform, resample_rate, title="Kaiser Window Fast (librosa)") .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_012.png :alt: Kaiser Window Fast (librosa) (sample rate: 32000 Hz) :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_012.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 318-322 .. code-block:: default mse = torch.square(resampled_waveform - librosa_resampled_waveform).mean().item() print("torchaudio and librosa kaiser fast MSE:", mse) .. rst-class:: sphx-glr-script-out .. code-block:: none torchaudio and librosa kaiser fast MSE: 2.5200744248601027e-05 .. GENERATED FROM PYTHON SOURCE LINES 323-333 Performance Benchmarking ------------------------ Below are benchmarks for downsampling and upsampling waveforms between two pairs of sampling rates. We demonstrate the performance implications that the ``lowpass_filter_wdith``, window type, and sample rates can have. Additionally, we provide a comparison against ``librosa``\ ’s ``kaiser_best`` and ``kaiser_fast`` using their corresponding parameters in ``torchaudio``. .. GENERATED FROM PYTHON SOURCE LINES 333-338 .. code-block:: default print(f"torchaudio: {torchaudio.__version__}") print(f"librosa: {librosa.__version__}") print(f"resampy: {resampy.__version__}") .. rst-class:: sphx-glr-script-out .. code-block:: none torchaudio: 0.13.0 librosa: 0.9.2 resampy: 0.2.2 .. GENERATED FROM PYTHON SOURCE LINES 340-369 .. code-block:: default def benchmark_resample_functional( waveform, sample_rate, resample_rate, lowpass_filter_width=6, rolloff=0.99, resampling_method="sinc_interpolation", beta=None, iters=5, ): return timeit.timeit( stmt=''' torchaudio.functional.resample( waveform, sample_rate, resample_rate, lowpass_filter_width=lowpass_filter_width, rolloff=rolloff, resampling_method=resampling_method, beta=beta, ) ''', setup='import torchaudio', number=iters, globals=locals(), ) * 1000 / iters .. GENERATED FROM PYTHON SOURCE LINES 371-403 .. code-block:: default def benchmark_resample_transforms( waveform, sample_rate, resample_rate, lowpass_filter_width=6, rolloff=0.99, resampling_method="sinc_interpolation", beta=None, iters=5, ): return timeit.timeit( stmt='resampler(waveform)', setup=''' import torchaudio resampler = torchaudio.transforms.Resample( sample_rate, resample_rate, lowpass_filter_width=lowpass_filter_width, rolloff=rolloff, resampling_method=resampling_method, dtype=waveform.dtype, beta=beta, ) resampler.to(waveform.device) ''', number=iters, globals=locals(), ) * 1000 / iters .. GENERATED FROM PYTHON SOURCE LINES 405-429 .. code-block:: default def benchmark_resample_librosa( waveform, sample_rate, resample_rate, res_type=None, iters=5, ): waveform_np = waveform.squeeze().numpy() return timeit.timeit( stmt=''' librosa.resample( waveform_np, orig_sr=sample_rate, target_sr=resample_rate, res_type=res_type, ) ''', setup='import librosa', number=iters, globals=locals(), ) * 1000 / iters .. GENERATED FROM PYTHON SOURCE LINES 431-480 .. code-block:: default def benchmark(sample_rate, resample_rate): times, rows = [], [] waveform = get_sine_sweep(sample_rate).to(torch.float32) args = (waveform, sample_rate, resample_rate) # sinc 64 zero-crossings f_time = benchmark_resample_functional(*args, lowpass_filter_width=64) t_time = benchmark_resample_transforms(*args, lowpass_filter_width=64) times.append([None, f_time, t_time]) rows.append("sinc (width 64)") # sinc 6 zero-crossings f_time = benchmark_resample_functional(*args, lowpass_filter_width=16) t_time = benchmark_resample_transforms(*args, lowpass_filter_width=16) times.append([None, f_time, t_time]) rows.append("sinc (width 16)") # kaiser best kwargs = { "lowpass_filter_width": 64, "rolloff": 0.9475937167399596, "resampling_method": "kaiser_window", "beta": 14.769656459379492, } lib_time = benchmark_resample_librosa(*args, res_type="kaiser_best") f_time = benchmark_resample_functional(*args, **kwargs) t_time = benchmark_resample_transforms(*args, **kwargs) times.append([lib_time, f_time, t_time]) rows.append("kaiser_best") # kaiser fast kwargs = { "lowpass_filter_width": 16, "rolloff": 0.85, "resampling_method": "kaiser_window", "beta": 8.555504641634386, } lib_time = benchmark_resample_librosa(*args, res_type="kaiser_fast") f_time = benchmark_resample_functional(*args, **kwargs) t_time = benchmark_resample_transforms(*args, **kwargs) times.append([lib_time, f_time, t_time]) rows.append("kaiser_fast") df = pd.DataFrame(times, columns=["librosa", "functional", "transforms"], index=rows) return df .. GENERATED FROM PYTHON SOURCE LINES 482-492 .. code-block:: default def plot(df): print(df.round(2)) ax = df.plot(kind="bar") plt.ylabel("Time Elapsed [ms]") plt.xticks(rotation = 0, fontsize=10) for cont, col, color in zip(ax.containers, df.columns, mcolors.TABLEAU_COLORS): label = ["N/A" if v != v else str(v) for v in df[col].round(2)] ax.bar_label(cont, labels=label, color=color, fontweight="bold", fontsize="x-small") .. GENERATED FROM PYTHON SOURCE LINES 493-495 Downsample (48 -> 44.1 kHz) ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 496-500 .. code-block:: default df = benchmark(48_000, 44_100) plot(df) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_013.png :alt: audio resampling tutorial :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_013.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none librosa functional transforms sinc (width 64) NaN 2.37 0.34 sinc (width 16) NaN 1.15 0.32 kaiser_best 88.67 2.08 0.37 kaiser_fast 10.35 1.85 0.34 .. GENERATED FROM PYTHON SOURCE LINES 501-503 Downsample (16 -> 8 kHz) ~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 504-508 .. code-block:: default df = benchmark(16_000, 8_000) plot(df) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_014.png :alt: audio resampling tutorial :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_014.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none librosa functional transforms sinc (width 64) NaN 1.02 0.69 sinc (width 16) NaN 0.50 0.27 kaiser_best 16.64 1.19 0.72 kaiser_fast 4.63 0.66 0.31 .. GENERATED FROM PYTHON SOURCE LINES 509-511 Upsample (44.1 -> 48 kHz) ~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 512-516 .. code-block:: default df = benchmark(44_100, 48_000) plot(df) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_015.png :alt: audio resampling tutorial :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_015.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none librosa functional transforms sinc (width 64) NaN 2.28 0.34 sinc (width 16) NaN 1.14 0.32 kaiser_best 38.46 1.98 0.36 kaiser_fast 10.93 1.78 0.33 .. GENERATED FROM PYTHON SOURCE LINES 517-519 Upsample (8 -> 16 kHz) ~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 520-524 .. code-block:: default df = benchmark(8_000, 16_000) plot(df) .. image-sg:: /tutorials/images/sphx_glr_audio_resampling_tutorial_016.png :alt: audio resampling tutorial :srcset: /tutorials/images/sphx_glr_audio_resampling_tutorial_016.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none librosa functional transforms sinc (width 64) NaN 0.47 0.25 sinc (width 16) NaN 0.38 0.17 kaiser_best 15.44 0.64 0.25 kaiser_fast 4.61 0.52 0.17 .. GENERATED FROM PYTHON SOURCE LINES 525-539 Summary ~~~~~~~ To elaborate on the results: - a larger ``lowpass_filter_width`` results in a larger resampling kernel, and therefore increases computation time for both the kernel computation and convolution - using ``kaiser_window`` results in longer computation times than the default ``sinc_interpolation`` because it is more complex to compute the intermediate window values - a large GCD between the sample and resample rate will result in a simplification that allows for a smaller kernel and faster kernel computation. .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 4.363 seconds) .. _sphx_glr_download_tutorials_audio_resampling_tutorial.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: audio_resampling_tutorial.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: audio_resampling_tutorial.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_